ETHZ-UZh-Sbg Arithmetic and Geometry Research Group

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**ProDoc-Archive**

**People:**

Chairman:

Wüstholz, Gisbert, Prof. Dr.

*Administration*:

Lachmuth, Christa

Professors:

Ayoub, Joseph, Prof. Dr.

Doran, Brent, Prof. Dr.

Imamoglu, Özlem, Prof. Dr.

Kowalski, Emmanuel, Prof. Dr.

Kresch, Andrew, Prof. Dr.

Graduate Students holding a grant:

Fazlija, Bledar

Lamberti, Lisa

Steiger, Andreas

Other Graduate Students:

Ditchen, Jakob

Gallauer, Martin

Jermann, Jonas

Löffel, Benny

Pepin Lehalleur, Simon

Paulin, Roland

Pham Duc, Hiep

Rassias, Michael

Huicochea, Mario

Vezzani, Alberto

Lecturer and Postdocs:

Bruin, Pieter Jan, Dr.

Former members of the ProDoc:

Choudhury, Utsav, Dr.

Froyshov, Kim, Prof. Dr.

Fuchs, Clemens, Prof. Dr.

Giansiracusa, Noah, Dr.

Haase, Daniel, Dr.

Habegger, Philipp, Prof. Dr.

Hörmann, Fritz, Dr.

von Känel, Rafael, Dr.

Kühne, Lars, Dr.

Momot, Aleksander, Dr.

Preu, Thomas, Dr.

Scheimbauer, Claudia

Skowera, Jonathan, Dr.

Viada-Aehle, Evelina, Prof. Dr.

Yu, Jun, Dr.

Wang, Mingxi, Dr.

Zannier, Umberto, Prof. Dr.

**Research Modules:**

Number Theory:

Organizers: Prof. Dr. Gisbert Wüstholz and PD Dr. Clemens Fuchs.

In a first phase of our research project we shall study two types of problems. The first problem circles around the so-called Andre-Oort conjecture. This conjecture is located at the borderline between number theory and arithmetic algebraic geometry. We have been continuously studying various aspects of this question in the past which is documented in recent publications. One of the motivations for our studies is that there is a close connection to transcendence theory. This theory originates in the classification of real and complex numbers such as rational numbers versus irrational numbers, algebraic versus non-algebraic numbers where a real or complex number is called algebraic if it is a root of a polynomial with integral coefficients. Transcendence theory deals with non-algebraic, also called transcendental numbers. They were first mentioned by Euler, as it seems. Most numbers are transcendental but it is almost impossible to verify the transcendence of any particular given number. Coming back to the Andre-Oort conjecture it seems that two young researchers, Yafaev and Klingler, have reduced in a not yet published paper the conjecture to an even more famous and more difficult conjecture in analytic number theory. This conjecture, the Riemann hypothesis, has been open since almost 150 years and there is no hope that we shall see a proof in the near future. There is one very simple case in which the Andre-Oort conjecture has been proved by Andre himself unconditionally. The proof relies on class field theory, algebraic geometry and on a result in transcendence theory. This is our starting point. In an ambitious PhD project a very talented graduate student tries to extend the existing proof to a more general situation and to exhaust the method. As a first step a conjecture of Wuestholz in transcendence theory which generalizes a theorem of Masser and which is used in Andre's proof has to be proved. The methods needed for the transcendence part of the project are available. It is clear that the remaining part can be done subject to a number of technical difficulties. In the last three decades another system of numbers, the so-called p-adic numbers, have been studied very intensively in various parts of mathematics. They are defined for each prime number p and they are particularly useful for arithmetic studies. Also here the classification system for numbers apply and one can speak of transcendental p-adic numbers. In the second part of the research project another graduate student started to work on the analytic subgroup theorem, the most powerful existing theorem in transcendence theory. The theorem gives in a very systematic and conceptual way a large class of transcendental numbers. The goal of the project is to obtain the p-adic analogue of the analytic subgroup theorem and to deduce new classes of transcendental numbers. In the framework of the present research project there are at the moment four further ongoing PhD projects. However so far they are not financed within this research project. Further PhD projects are expected.

Projective Stacks:

Organizer: Prof. Dr. Andrew Kresch.

Algebraic varieties are the solution sets to systems of polynomial equations. An important case is that of homogeneous polynomial equations, defining projective algebraic varieties. Algebraic stacks are more general objects, not so readily encoded by means of equations. This project seeks to identify and study algebraic stacks which could be called "projective" and use the findings about algebraic stacks to address classical problems. Classically one knows that space can be extended by adding "points at infinity". Then, for instance, we may assert that parallel lines will intersect at a point at infinity. With algebraic stacks, point are endowed with the extra information of a stabilizer group. A typical geometric question about projective stacks could be, given a stack for which we have a good understanding of the points in ordinary space, can we understand the stabilizer groups at the points at infinity? The questions become more subtle and the answers more interesting in situations that are far away from classical geometry, for instance when working over a base field of positive characteristic, or in arithmetic geometry (that is, over the base ring of integers).

Diophantine and Algebraic Geometry:

Organizers: Prof. Dr. Gisbert Wüstholz and Prof. Dr. Brent Doran.

In this project we study classical algebro-geometric problems. We have two different aspects in mind. One part deals with geometric problems which come up in the classification of algebraic varieties and in birational geometry. The main tools is the motivic homotopy theory of Morel and Voevodsky. Another part is a PhD project in diophantine geometry. Here techniques from projective algebraic geometry, arithmetic intersection theory and diophantine approximations have to be combined to attack an old problem of Baker and Coates on effective bounds for the height of integral points on general hyperelliptic curves.

Cluster Categories:

Organizer: Prof. Dr. Karin Baur.

This project investigates new geometrical models for orbit categories of bounded derived categories such as cluster categories. The cluster category associated to a path algebra A is defined as the orbit category under a certain autoequivalence of the bounded derived category of A-modules. Cluster categories can be modelled using triangulations of regular polygons. Similarly, m-cluster categories can be modelled by dividing polygons into smaller polygons. Cluster categories have been introduced because of their combinatorial similarity with cluster algebras. As such they provide an example of a categorification, i.e. of the process of associating a category to an algebraic object. The questions arising here naturally are: What is the dictionary between the properties of the original (algebraic) object and the properties of the category and of the associated functors? How do results from the first setting translate to the categorical setting?

Local and globald equidisbribution for arithmetic objects:

Organizer: Prof. Dr. Emmanual Kowalski

The research goals of the proposal concern some important aspects of analytic number theory where the notion of equidistribution is of high importance, and where important links with probability theory arise. Whereas many existing works can be interpreted in this manner, they do not usually highlight this in a systematic manner. However, developing more thoroughly the general framework seems to be likely to be very useful, in particular to understand in greater depth some cases where, in the current state of knowledge, only conjectures supported by numerical or heuristic arguments exist. The project proposes to look at these types of problems in the following situations: •In the setting of the conjectures concerning the distribution of values of L-functions, based on theoretical, heuristic and numerical evidence, where Random Matrix Theory plays an important role, many fundamental problems remain unsolved, but the recent introduction of the notion of ``mod-Gaussian'' and ``mod-Poisson'' convergence of sequences of random variables suggests a number of new relations with probability, and (at least in the setting of function fields) hopes for new approaches. •Quite general problems have been treated more systematically recently by generalizing the sieve methods of classical analytic number theory, but the applications of these techniques are far from being exhausted. The links with counting problems of hyperbolic type, recently investigated by many authors, and with random walks on discrete groups, will be looked-at in much greater detail. •A very natural question of analytic number theory, which has not yet been investigated in depth, is to consider families of (global) L-functions, say associated with automorphic representations of GL(n), and ask about the distribution, either for a fixed prime or uniformly, of the local components of the representations in the spectrum of the local p-adic group. This question seems, however, to be likely to be of great importance in understanding higher rank L-functions. •One can define various invariants of finite groups using ideas of probabilistic group theory, and their distribution in the case of Galois groups, and in particular for families of number fields, becomes a problem intricately related with sieve techniques and questions about L-functions.

**Guests:**

Jean-Pierre Wintenberger (Strasbourg), 16.02.2009-30.05.2009

Carlo Gasbarri (Università di Roma "Tor Vergata"), 02.04.2009-03.04.2009

Valentin Blomer (Toronto), 10.05.2009-15.05.2009

Bas Edixhoven (Leiden), 10.05.2009-15.05.2009

Hélène Esnault (Duisburg-Essen), 10.05.2009-15.05.2009

Jay Jorgensen (CCNY), 10.05.2009-15.05.2009

Chandrashekhar Khare (UCLA), 10.05.2009-15.05.2009

Bruno Klingler (Princeton), 10.05.2009-15.05.2009

Maxim Kontsevich (IHES), 10.05.2009-15.05.2009

Jürg Kramer (Berlin), 10.05.2009-15.05.2009

Kenneth A. Ribet (Berkeley), 10.05.2009-15.05.2009

Yuri Tschinkel (NYU), 10.05.2009-15.05.2009

Eckhard Viehweg (Duisburg-Essen), 10.05.2009-15.05.2009

Andrei Yafaev (UCL), 10.05.2009-15.05.2009

Yuri Zarhin (Penn State), 02.08.2009-15.08.2009

Michael Stoll (Bayreuth), 12.08.2009-16.08.2009

Sergej Gorchinskiy (Russian Academy of Science, Moscow), 01.09.2009-28.02.2010

Umberto Zannier (SNS Pisa), 02.06.2009-07.06.2009 and 01.10.2009-28.10.2009

Tzanko Matev (Bayreuth), 25.10.2009-31.10.2009

Hironori Shiga (Waseda University Tokyo), 07.01.2010-15.01.2010

Florian Luca (UNAM), 01.03.2010-09.03.2010

Shanta Laishram (IIT Dehli), 19.05.2010-01.07.2010

N. Saradha (TIFR), 20.05.2010-06.06.2010

Speakers at the FIM-Workshop "Rational Points - Theory & Experiment", 25.05.2010-29.05.2010

Laurent Berger (Lyon), 18.07.2010-23.07.2010

Giovanni di Matteo (Lyon), 18.07.2010-23.07.2010

Sergey Gorchinskiy (Moscow), 15.07.2010-27.07.2010

Sergey Rybakov (Moscow), 15.07.2010-27.07.2010

Anna-Maria von Pippich (Basel), 23.09.2010-24.09.2010

Patrick Tuen Wai Ng (Hong Kong), 18.10.2010-25.10.2010

Speakers at the FIM-Workshop "Exponential sums over finite fields and applications", 01.11.2010-05.11.2010

Alain Togbe (Purdue North Central), 02.11.2010-05.11.2010

Winfried Kohnen (Heidelberg), 29.04.2011

Kunrui Yu (Hong Kong University of Science and Technology), 04.05.2011-04.06.2011

Paula Tretkoff (Texas A&M University), 09.05.2011-10.05.2011

Solomon Friedberg (Boston College), 14.05.2011-21.05.2011

Sergey Gorchinskiy (Moscow), 09.07.2011-20.07.2011

Annette Huber-Klawitter (Freiburg), 16.07.2011-19.07.2011

Stefan Müller-Stach (Mainz), 16.07.2011-19.07.2011

Sergey Rybakov (Moscow), 13.07.2011-19.07.2011

Sonia Samol (Mainz), 13.07.2011-19.07.2011

Konrad Völkel (Freiburg), 13.07.2011-19.07.2011

Jonas von Wangenheim (Freiburg), 13.07.2011-19.07.2011

Thomas Weißschuh (Mainz), 13.07.2011-19.07.2011

Peter Wieland (Freiburg), 13.07.2011-19.07.2011

Cormac O'Sullivan (Bronx Community College / CUNY Graduate Center), 25.09.-01.10.2011

Ngô Bao Châu (University of Chicago), 25.10.-27.10.2011

Stephen Kudla (University of Toronto), 25.10.-27.10.2011

Guy Henniart (Université Paris-Sud 11), 25.10.-27.10.2011

Philipp Habegger (University of Frankfurt), 02.12.2011

Lars Kühne (SNS Pisa), 31.01.2012

Winfried Khonen (Heidelberg), 28.03.2012

Umberto Zannier (SNS Pisa), 06.03.2012-09.03.2012

Jeffrey Hoffstein (Brown University), 29.03.2012

Sergey Gorchinskiy (Moscow), 10.04.2012-14.04.2012

Javier Fresan (Paris), 13.09.2013

Sergey Gorchinskiy (Moscow), 28.09.2012

Konrad Völkel (Universität Freiburg), 07.12.2012

Ishai Dan-Cohen (Universität Duisburg-Essen), 15.11.2012

Annette Werner (Göttingen), 23.11.2012

Konrad Völkel (Freiburg), 06.12.2012

Clemens Fuchs (Salzburg), 17.02.2013-19.02.2013

Marc Levine (Duisburg-Essen), 23.05.2013-07.06.2013

Lars Kühne (SNS Pisa), 24.05.2013-07.06.2013

Rafael von Kanel (Paris), 24.05.2013-07.06.2013

Ngaiming Mok (Hong Kong), 24.05.2013-07.06.2013

Ioulia Beloshapka (Moscow), 04.07.2013-13.07.2013

Clemens Fuchs (Salzburg), 19.08.2013-22.08.2013

**Publications:**

For further publications and (in particular) preprints see the personal web pages of the participating members of the ProDoc. •A. Momot: On the classification of complex tori arising from real Abelian surfaces, Abh. Math. Sem. Univ. Hambg. 79 (2009), 283-298. •C. Fuchs, T.N. Shorey: Divisibility properties of generalized Laguerre polynomials, Indag. Math. (N.S.) 20 (2009), 217-231. •C. Fuchs: Polynomial-exponential equations involving multi-recurrences, Stud. Sci. Math. Hungar. 46 (2009), 377-398. •C. Fuchs, R.F. Tichy, V. Ziegler: On quantitative aspects of the unit sum number problem, Arch. Math. 93 (2009), 259-268. •R. von Känel: An effective proof of the hyperelliptic Shafarevich conjecture and applications, PhD thesis, ETH Zurich, 2010. •T. Preu: Transcendental Brauer-Manin obstruction for a diagonal quartic surface, PhD thesis, Univ. of Zurich, 2010. •C. Fuchs, R. von Känel, G. Wüstholz: An effective Shafarevich theorem for elliptic curves, Acta Arith. 148 (2011), 189-203. •C. Fuchs, A. Pethö: Composite rational functions having a bounded number of zeros and poles, Proc. AMS 139 (2011), 31-38. •C. Fuchs: Angle trisection with Origami and related topics, Elem. Math. 66 (2011), 121-136. •M. Wang: Rational points and transcendental points, PhD thesis, ETH Zurich, 2011. •L. Kühne: An effective result of André-Oort type, PhD thesis, ETH Zurich, 2012. •A. Momot: Density of rational points on commutative algebraic groups and small transendence degree, PhD thesis, ETH Zurich, 2012. •C. Fuchs, U. Zannier: Composite rational functions expressible with few terms, J. Eur. Math. Soc. 14 (2012), 175-208. •A. Dujella, C. Fuchs: On a problem of Diophantus for rationals, J. Number Theory 132 (2012), 2075-2083. •H. Pham: New progress in p-adic transcendence theory, PhD thesis, ETH Zurich, 2013. •L. Kühne: An effective result of André-Oort type, Ann. Math. (2) 176 (2012), 651-671. •C. Fuchs, T.N. Shorey: Divisibility properties of hypergeometric polynomials, J. Comb. Number Theory 4 (2012), 1-10. •J. Jermann: Interlacing property of the zeros of j_n(tau), Proc. AMS 140 (2013), 3385-3396. •T.W. Ng, M. Wang: Ritt's theory on the unit disk, Forum Math. 25 (2013), 821-851. •T. Preu: Example of a transcendental 3-torsion Brauer-Manin obstruction on a diagonal quartic surface, LMS Lecture Note Series "Torsors, étale homotopy and applications to rational points", to appear. •J. Skowera: Bialynicki-Birula decomposition of Deligne Mumford stacks, Proc. AMS 141 (2013), 1933-1937. •Y.F. Bilu, C. Fuchs, F. Luca, Á. Pintér: Combinatorial Diophantine equations and a refinement of a theorem on separated variables equations, Publ. Math. Debrecen 82 (2013), 219-254. •G. Wüstholz: Leibniz' conjecture, periods & motives, Colloquium De Giorgi 2009 (Edizioni della Normale, 2012 edition (May 28, 2012). •M. Wang, G. Wüstholz: Meromorphic Maps on Riemann Surfaces and Transcendence, Sovremennye Problemy Matematiki 17 (2013), 113-134. •M. Walter, B. Doran, D. Gross, M. Christandl: Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information, Science 340 (2013), 1205-1208. •J. Ayoub, S. Zucker: Relative Artin motives and the reductive Borel-Serre compactification of a locally symmetric variety, Invent. Math. 188 (2012), 277–427. •J. Ayoub: Le carré du foncteur de dualité est monoïdal, Comm. Algebra 39 (2011), 1528–1535. •J. Ayoub: The n-motivic t-structures for n=0, 1 and 2, Adv. Math. 226 (2011), 111–138. •J. Ayoub: Note sur les opérations de Grothendieck et la réalisation de Betti, J. Inst. Math. Jussieu 9 (2010), 225–263. •J. Ayoub, L. Barbieri-Viale: 1-motivic sheaves and the Albanese functor, J. Pure Appl. Algebra 213 (2009), 809–839. •W. Duke, Ö. Imamoglu, Á. Tóth: Real quadratic analogs of traces of singular moduli, Int. Math. Res. Not. IMRN 2011, no. 13, 3082–3094. •W. Duke, Ö. Imamoglu, Á. Tóth: Cycle integrals of the j-function and mock modular forms, Ann. of Math. (2) 173 (2011), no. 2, 947–981. •W. Duke, Ö. Imamoglu, Á. Tóth: Rational period functions and cycle integrals, Abh. Math. Semin. Univ. Hambg. 80 (2010), no. 2, 255–264. •Ö. Imamoglu, N. Raulf: On the behaviour of eigenvalues of Hecke operators, Math. Res. Lett. 17 (2010), no. 1, 51–67. •Ö. Imamoglu, C. O'Sullivan: Parabolic, hyperbolic and elliptic Poincaré series, Acta Arith. 139 (2009), no. 3, 199–228. •&OUml;. Imamoglu, Y. Martin: On characteristic twists of multiple Dirichlet series associated to Siegel cusp forms, Math. Z. 263 (2009), no. 2, 345–368. •J. B. Conrey, D.W. Farmer> Ö. Imamoglu: Palindromic random trigonometric polynomials, Proc. Amer. Math. Soc. 137 (2009), no. 5, 1835–1839. •A. Kresch: Flattening stratification and the stack of partial stabilizations of prestable curves, Bull. Lond. Math. Soc. 45 (2013), no. 1, 93–102. •B. Hassett, A. Kresch, Y. Tschinkel> Effective computation of Picard groups and Brauer-Manin obstructions of degree two K3 surfaces over number fields, Rend. Circ. Mat. Palermo (2) 62 (2013), no. 1, 137–151. •A. S. Buch, A. Kresch, H. Tamvakis: Quantum Giambelli formulas for isotropic Grassmannians, Math. Ann. 354 (2012), no. 3, 801–812. •A. Kresch, Y. Tschinkel: Effectivity of Brauer-Manin obstructions on surfaces, Adv. Math. 226 (2011), no. 5, 4131–4144. •A. Kresch> CW complexes for complex algebraic surfaces, Experiment. Math. 19 (2010), no. 4, 413–419. •A. S. Buch, A. Kresch, H. Tamvakis: Quantum Pieri rules for isotropic Grassmannians, Invent. Math. 178 (2009), no. 2, 345–405. •A. Kresch: On the geometry of Deligne-Mumford stacks, Algebraic geometry—Seattle 2005. Part 1, 259–271, Proc. Sympos. Pure Math., 80, Part 1, Amer. Math. Soc., Providence, RI, 2009. •K. Baur, V. Mazorchuk: Combinatorial analogues of ad-nilpotent ideals for untwisted affine Lie algebras, J. Algebra 372 (2012), 85–107. •K. Baur, L. Hille: On the complement of the Richardson orbit, Math. Z. 272 (2012), no. 1-2, 31–49. •K. Baur, R. J. Marsh: A geometric model of tube categories, J. Algebra 362 (2012), 178–191. •K. Baur, R. J. Marsh: Categorification of a frieze pattern determinant, J. Combin. Theory Ser. A 119 (2012), no. 5, 1110–1122. •K. Baur, A. Morea: Quasi-reductive (bi)parabolic subalgebras in reductive Lie algebras, Ann. Inst. Fourier (Grenoble) 61 (2011), no. 2, 417–451. •K. Baur, K. Erdmann, A. Parker: ?-filtered modules and nilpotent orbits of a parabolic subgroup in ON, J. Pure Appl. Algebra 215 (2011), no. 5, 885–901. •K. Baur, J. Draisma: Secant dimensions of low-dimensional homogeneous varieties, Adv. Geom. 10 (2010), no. 1, 1–29. •K. Baur, R. J. Marsh: Frieze patterns for punctured discs, J. Algebraic Combin. 30 (2009), no. 3, 349–379. •K. Baur, V. Ginzburg, I. Gordon, A. Parker, C. Stroppel: Preface [Cherednik algebras], Selecta Math. (N.S.) 14 (2009), no. 3-4, 323. •F. Jouve, E. Kowalski, D. Zywina: Splitting fields of characteristic polynomials of random elements in arithmetic groups, Israel J. Math. 193 (2013), no. 1, 263–307. •E. Kowalski: Crible en expansion, Séminaire Bourbaki: Vol. 2010/2011. Exposés 1027–1042. Astérisque 348 (2012), Exp. No. 1028, vii, 17–64. •E. Kowalski, A. Nikeghbali: Mod-Gaussian convergence and the value distribution of ?(12+it) and related quantities, J. Lond. Math. Soc. (2) 86 (2012), no. 1, 291–319. •J. S. Ellenberg, C. Hall, E. Kowalski: Expander graphs, gonality, and variation of Galois representations, Duke Math. J. 161 (2012), no. 7, 1233–1275. •E. Kowalski, A. Saha, J. Tsimerman: Local spectral equidistribution for Siegel modular forms and applications, Compos. Math. 148 (2012), no. 2, 335–384. •E. Kowalski, D. Zywina: The Chebotarev invariant of a finite group, Exp. Math. 21 (2012), no. 1, 38–56. •E. Kowalski: A survey of algebraic exponential sums and some applications. Motivic integration and its interactions with model theory and non-Archimedean geometry, Volume II, 178–201, London Math. Soc. Lecture Note Ser., 384, Cambridge Univ. Press, Cambridge, 2011. •J. Jacod, E. Kowalski, A. Nikeghbali: Mod-Gaussian convergence: new limit theorems in probability and number theory, Forum Math. 23 (2011), no. 4, 835–873. •C. Hall: An open-image theorem for a general class of abelian varieties With an appendix by Emmanuel Kowalski. Bull. Lond. Math. Soc. 43 (2011), no. 4, 703–711. •E. Kowalski: Averages of Euler products, distribution of singular series and the ubiquity of Poisson distribution, Acta Arith. 148 (2011), no. 2, 153–187. •E. Kowalski, A. Saha, J. Tsimerman: A note on Fourier coefficients of Poincaré series, Mathematika 57 (2011), no. 1, 31–40. •E. Kowalski, Y.-K. Lau, K. Soundararajan, J. Wu: On modular signs, Math. Proc. Cambridge Philos. Soc. 149 (2010), no. 3, 389–411. •E. Kowalski, A. Nikeghbali: Mod-Poisson convergence in probability and number theory, Int. Math. Res. Not. IMRN 2010, no. 18, 3549–3587. •E. Kowalski: Some aspects and applications of the Riemann hypothesis over finite fields, Milan J. Math. 78 (2010), no. 1, 179–220. •E. Kowalski: Poincaré and analytic number theory. The scientific legacy of Poincaré, 73–85, Hist. Math., 36, Amer. Math. Soc., Providence, RI, 2010. •E. Kowalski: Amplification arguments for large sieve inequalities, Arch. Math. (Basel) 94 (2010), no. 5, 443–457. •J. S. Ellenberg, C. Elsholtz, C. Hall, E. Kowalski: Non-simple abelian varieties in a family: geometric and analytic approaches, J. Lond. Math. Soc. (2) 80 (2009), no. 1, 135–154. •L. Lamberti: On cluster categories and related topics, PhD thesis, ETH Zurich, 2013. •L. Lamberti: Repetitive higher cluster categories of type A_n, Journal of Algebra and its Applications, to appear. •L. Lamberti: A geometric interpretation of the triangulated structure of m-cluster categories, Communications in Algebra, to appear. •L. Lamberti: A combinatorial model for the cluster categories of type E, preprint, 2013. •L. Lamberti: Chebyshev polynomials and tensor diagrams, preprint, 2013. •M. Huicochea: Extending Nathanson heights to arbitrary finite fields, Integers 12 (2012), no. 4, 669-675, A13. •U. Choudhury, J. Skowera: Motivic decomposition of cellular Deligne-Mumford stacks, Communications in Algebra, to appear. •U. Choudhury: Motives of Deligne-Mumford stacks, Adv. Math. 231 (2012), no. 6, 3094–3117. •J-S. Huang, J. Yu: Klein four-subgroups of Lie algebra automorphisms, Pacific J. Math. 262 (2013), no. 2, 397-420. •J. An, J. Yu, J-K. Yu: On the dimension datum of a subgroup and its application to isospectral manifolds, J. Differential Geom. 94 (2013), no. 1, 59-85. •J. Yu: Elementary abelian 2-subgroups of compact Lie groups, Geometriae Dedicata, to appear. •J. Yu: Dimension data of closed subgroups and algebraic vector bundles on punctured affine spaces and smooth quadrics, PhD thesis, ETH Zurich, 2012.

**Seminars:**

*FS 2013*:

30.05.2013: Prof. Ngaiming Mok (The University of Hong Kong) Holomorphicisometries on bounded domains

23.05.2013: Prof. Marc Levine (Universität Duisburg-Essen) An introduction to motivic homotopy theory

16.05.2013: Dr. Rafael von Känel (Institut des Hautes Études Scientifiques, I.H.É.S.) Discriminants and small points of curves

25.04.2013: Sam Molcho (Brown University) Localization for log stable maps

18.03.2013-23.03.2013: Equidistribution in Number Theory and Dynamics

*HS 2012*:

07.12.2012: Konrad Völkel (Universität Freiburg) Matsumoto's Theorem in Motivic Homotopy Theory

15.11.2012: Ishai Dan-Cohen (Universität Duisburg-Essen) Explicit Chabauty-Kim theory for the thrice punctured line in depth two

01.11.2012: Jonathan Skowera (UZH) Decompositions and integral cycles of algebraic stacks

25.10.2012: Lars Kühne (ETHZ) Linear independence results for odd zeta values

18.10.2012: Roland Paulin (ETHZ) Criteria for linear independence

*FS 2012*:

29.03.2012: Jeffrey Hoffstein (Brown University) Multiple Dirichlet Day Dreams

08.03.2012: Umberto Zannier (SNS Pisa) Sharpening 'Manin-Mumford' for certain algebraic groups of dimension 2

*HS 2011*:

10.11.2011: Roland Paulin (ETH Zürich) Minimal degree of morphisms between curves

26.10.2011: Heinz-Hopf Symposium in HG D7.2: Ngô Bao Châu (University of Chicago) at 11 am: Abelian fibration associated with the geometric side of the trace formula, Stephen Kudla (University of Toronto) at 3 pm: Modular generating series for arithmetic special cycles, Guy Henniart (Université Paris-Sud 11) at 4 pm: Modular Langlands correspondence: new avatars

29.09.2011: Cormac O'Sullivan (Bronx Community College / CUNY Graduate Center) Taylor coefficients of modular forms

*FS 2011*:

09.06.2011: Martin Gallauer (UZH) Preparation for Alpbach III: proof that standard cohomology theories obey axioms, proof of theorem of de Rahm

07.06.2011 from 15:15-17:00 in HG G 19.1: Mario Huicochea, Hiep Pham Duc (ETHZ) Preparation for Alpbach II: axiomatic theory of (co-)homology theories on smooth manifolds, introduction of some standard (co-)homology theories on smooth manifolds

26.05.2011: Bledar Fazlija (ETHZ) Preparation for Alpbach I: integration of forms over cycles on smooth manifolds, theorem of Stokes, basics on homological algebra, integration of cohomology classes against homology classes

19.05.2011: Solomon Friedberg (Boston College) 15:15-16:00: Metaplectic Eisenstein Series and Multiple Dirichlet Series. Abstract: In this hour I give an introduction to metaplectic Eisenstein series and multiple Dirichlet series. No prior background concerning these topics will be assumed. 16:15-17:00: Ice Models and Automorphic Forms. Abstract: In this hour I show how ice models from statistical mechanics can be used to model automorphic forms and also multiple Dirichlet series that are related to metaplectic Eisenstein series. Once again, the relevant concepts will be described from first principles.

10.05.2011 from 17:15-18:15 in HG G 43 (HWZ): Paula Tretkoff (Texas A&M University) An Introduction to the Analytic Subgroup Theorem and its Applications (part II)

09.05.2011 from 17:15-18:15 in HG G 43 (HWZ): Paula Tretkoff (Texas A&M University) An Introduction to the Analytic Subgroup Theorem and its Applications (part I)

07.05.2011 from 11:00-12:00 in GR A3 32 at EPFL: Paula Tretkoff (Texas A&M University) Variations of Hodge Structure and the Analytic Subgroup Theorem. This first talk of the Minicourse is part of the ETH Number Theory Days 2011 (for more information see here).

07.04.2011: Martin Gallauer (Uni Zürich) Lefschetz-Verdier trace formula and a generalization of a theorem of Fujiwara

31.03.2011: Gergely Berczi (University of Oxford) Recent progress on the Green-Griffiths-Lang conjecture

10.03.2011: Lisa Lamberti (ETH Zurich) Cluster categories and their geometrical model

03.03.2011: Rafael von Känel (ETH Zurich) On the Modular Degree Conjecture

24.02.2011: Mingxi Wang (ETH Zurich) Dynamical Mordell-Lang for the polydisk

*HS 2010*:

16.12.2010: Jörg Jahnel (Universität Siegen) K3 surfaces and their Picard groups

09.12.2010: Thomas Preu (Uni Zürich) The Brauer-Manin Obstruction

25.11.2010: Noah Giansiracusa (Brown University) Conformal blocks and rational normal curves

04.11.2010: Patrik Hubschmid (ETH Zurich) The André-Oort Conjecture for Drinfeld moduli spaces

14.10.2010: Gyula Karolyi (Eötvös University, Budapest / EPFL) On the Combinatorial Nullstellensatz and its applications (part II)

07.10.2010: Gyula Karolyi (Eötvös University, Budapest / EPFL) On the Combinatorial Nullstellensatz and its applications (part I)

23.09.2010: Anna von Pippich (Basel) Elliptic Eisenstein series

*FS 2010*:

03.06.2010: Dzmitry Doryn (Essen) Cohomology of graph hypersurfaces and counting of points

06.05.2010 Jun Yu (ETH Zürich): On the dimension data problem (Summary of the talk), Rafael von Känel (ETH Zürich): An effective Shafarevich theorem for elliptic curves

29.04.2010 Paul Ziegler (ETH Zürich) Classification of F-Zips

13.04.2010: Heinrich Massold (Zürich) Transcendence degrees and algebraic approximation

25.03.2010: Clemens Fuchs (ETH Zürich) On decomposable lacunary rational functions (part III)

18.03.2010: Clemens Fuchs (ETH Zürich) On decomposable lacunary rational functions (part II)

11.03.2010: Charles Doran (University of Alberta, Edmonton) Normal forms for Lattice Polarized K3 Surfaces and the Kuga-Satake Hodge Conjecture

04.03.2010: Clemens Fuchs (ETH Zürich) On decomposable lacunary rational functions (part I)

14.01.2010: Hironori Shiga (Waseda University Tokyo) Period Differential Equations for Some Families of K3 Surfaces in Connection with the Hilbert Modular Group for Q(Sqrt[5]) (Prof. Shiga's script for the talk is available)

*HS 2009*:

10.12.2009: Fritz Hörmann (ETH Zürich) Arithmetic and geometric volume of Shimura varieties of orthogonal type (part II)

03.12.2009: Fritz Hörmann (ETH Zürich) Arithmetic and geometric volume of Shimura varieties of orthogonal type (part I)

26.11.2009: Daniel Haase (ETH Zürich) Arithmetic Group Determinants (Slides for the talk)

19.11.2009: Maria Petkova (ETH Zürich) Ball Quotient Curves and Quaternion Algebras

12.11.2009: Simon Pepin-Lehalleur (Université Paris 13) Triangulated categories of motives and compactifications of Shimura varieties

29.10.2009: Tzanko Matev (Bayreuth) The p-adic analytic subgroup theorem

26.10.2009: Umberto Zannier (SNS Pisa) Some problems of integral points on varieties over function fields (part IV) (exceptional time and place: the talk takes place on monday in room HG G19.2 at 15-17h).

22.10.2009: Umberto Zannier (SNS Pisa) Some problems of integral points on varieties over function fields (part III)

15.10.2009: Umberto Zannier (SNS Pisa) Some problems of integral points on varieties over function fields (part II)

08.10.2009: Umberto Zannier (SNS Pisa) Some problems of integral points on varieties over function fields (part I)

24.09.2009 Alena Pirutka (ENS/Paris 11) R-equivalence on low degree complete intersections and rationally simply connected varieties

*FS 2009*:

07.05.2009: Utsav Choudhury (Uni Zürich) Rational connectivity and A1-connectivity

23.04.2009 Mingxi Wang (ETH) Meromorphic maps on Riemann surfaces and transcendence

02.04.2009 Carlo Gasbarri (Univesità di Roma "Tor Vergata") Transcendence and Nevanlinna theory

26.03.2009 René Birkner (FU Berlin) An introduction to toric Hilbert schemes

19.03.2009 Jean-Pierre Wintenberger (University of Strasbourg) Construction of the Galois representation associated to a weight 2 modular form (part IV)

12.03.2009 Jean-Pierre Wintenberger (University of Strasbourg) Construction of the Galois representation associated to a weight 2 modular form (part III)

05.03.2009 Jean-Pierre Wintenberger (University of Strasbourg) Construction of the Galois representation associated to a weight 2 modular form (part II)

26.02.2009 Jean-Pierre Wintenberger (University of Strasbourg) Construction of the Galois representation associated to a weight 2 modular form (part I)

(Notes (updated 07.05.2009) from Prof. Wintenberger are available)

*Previously*:

Aleksander Momot: Über eine Variante der Schanuel'schen Vermutung für Funktionenkörper: Formulierung der Schanuel'schen Vermutung und Konsequenzen, Freitag, 03. November 2006 um 11:10 Uhr

Aleksander Momot: Über eine Variante der Schanuel'schen Vermutung für Funktionenkörper: Beweisskizze und Beweis 1. Teil, Freitag, 06. November 2006 um 16:15 Uhr

Walter Gubler (Universität Dortmund): Berkovich Räume und tropische analytische Geometrie: Teil 1 (Minikurs im Rahmen der Zurich Graduate School of Mathematics), Montag, 13. November 2006 von 16:15 - 17:30 Uhr, HG G 19.2

Walter Gubler (Universität Dortmund): Berkovich Räume und tropische analytische Geometrie: Teil 2 (Minikurs im Rahmen der Zurich Graduate School of Mathematics), Dienstag, 14. November 2006 von 15:15 - 16:30 Uhr, HG G 19.2

Aleksander Momot: Über eine Variante der Schanuel'schen Vermutung für Funktionenkörper: Beweis des Hauptresultates, Montag, 20. November 2006 um 17:15 Uhr

Winfried Kohnen (Universität Heidelberg): Sign changes of Fourier coefficients and Hecke eigenvalues of cusp forms (Vortrag im Rahmen des Zahlentheorie Seminars), Montag, 27. November 2006 um 16:15 Uhr, HG G 26.1

Aleksander Momot: Über eine Variante der Schanuel'schen Vermutung für Funktionenkörper: Beweis des Hauptresultates II, Montag, 04. Dezember 2006 um 16:00 Uhr

Aleksander Momot: Über eine Variante der Schanuel'schen Vermutung für Funktionenkörper: Beweis des Hauptresultates III, Montag, 11. Dezember 2006 um 16:15 Uhr

Gisbert Wüstholz: A (Wüstholz-style) proof of the Theorem of Lindemann, Monday, 08th of January 2007 at 16.15pm

Gisbert Wüstholz: A (Wüstholz-style) proof of the Theorem of Lindemann. II, Monday, 15th of January 2007 at 16.15pm

Gisbert Wüstholz: A (Wüstholz-style) proof of the Theorem of Lindemann. III. Into the Proof, Monday, 22th of January 2007 at 16.15pm

Gisbert Wüstholz: A (Wüstholz-style) proof of the Theorem of Lindemann. IV. Proof, Thursday, 08th of February 2007 at 14.15pm, HWZ (HG G 43)

Gisbert Wüstholz: A (Wüstholz-style) proof of the Theorem of Lindemann. V. Proof, Monday, 12th of February 2007 at 16.15pm, HWZ (HG G 43)

Gisbert Wüstholz: A (Wüstholz-style) proof of the Theorem of Lindemann. VI. Proof, Tuesday, 06th of March 2007 at 14.15pm, HWZ (HG G 43)

Gisbert Wüstholz: A (Wüstholz-style) proof of the Theorem of Lindemann. VII. QED, Wednesday, 07th of March 2007 at 11.10pm, HWZ (HG G 43)

Clemens Fuchs: Integral points on certain algebraic varieties, Thursday, 05th of April 2007 at 15.15pm, HG F 26.3

Clemens Fuchs: Integral points on certain algebraic varieties. II. Preliminaries and first reductions, Thursday, 26th of April 2007 at 15.15pm, HG F 26.3

Clemens Fuchs: Integral points on certain algebraic varieties. III. Filtration and properties, Thursday, 03rd of May 2007 at 15.15pm, HG F 26.3

Clemens Fuchs: Integral points on certain algebraic varieties. IV. Diophantine approximation part, Thursday, 10th of May 2007 at 15.15pm, HG F 26.3

Clemens Fuchs: Integral points on certain algebraic varieties. V. Other results and conjectures, Thursday, 24th of May 2007 at 15.15pm, HG F 26.3

Clemens Fuchs: Schlechte und gute Nachrichten für Herrn Hilbert, Tuesday, 19th of June 2007 at 17:15pm, HG D 5.2

Patrik Hubschmid: Definition and examples of general l-adic representations, Thursday, 30th of August 2007 at 13.30pm, HG G 19.1

Patrik Hubschmid: l-adic representations of number fields, Thursday, 30th of August 2007 at 15.30pm, HG G 19.1

Tobias Hahn: Equidistribution and L-functions, Part I, Friday, 31st of August 2007 at 13.30pm, HG G 19.1

Tobias Hahn: Equidistribution and L-functions, Part II, Friday, 31st of August 2007 at 15.30pm, HG G 19.1

Back to the main page.

Chairman:

Wüstholz, Gisbert, Prof. Dr.

Lachmuth, Christa

Professors:

Ayoub, Joseph, Prof. Dr.

Doran, Brent, Prof. Dr.

Imamoglu, Özlem, Prof. Dr.

Kowalski, Emmanuel, Prof. Dr.

Kresch, Andrew, Prof. Dr.

Graduate Students holding a grant:

Fazlija, Bledar

Lamberti, Lisa

Steiger, Andreas

Other Graduate Students:

Ditchen, Jakob

Gallauer, Martin

Jermann, Jonas

Löffel, Benny

Pepin Lehalleur, Simon

Paulin, Roland

Pham Duc, Hiep

Rassias, Michael

Huicochea, Mario

Vezzani, Alberto

Lecturer and Postdocs:

Bruin, Pieter Jan, Dr.

Former members of the ProDoc:

Choudhury, Utsav, Dr.

Froyshov, Kim, Prof. Dr.

Fuchs, Clemens, Prof. Dr.

Giansiracusa, Noah, Dr.

Haase, Daniel, Dr.

Habegger, Philipp, Prof. Dr.

Hörmann, Fritz, Dr.

von Känel, Rafael, Dr.

Kühne, Lars, Dr.

Momot, Aleksander, Dr.

Preu, Thomas, Dr.

Scheimbauer, Claudia

Skowera, Jonathan, Dr.

Viada-Aehle, Evelina, Prof. Dr.

Yu, Jun, Dr.

Wang, Mingxi, Dr.

Zannier, Umberto, Prof. Dr.

Number Theory:

Organizers: Prof. Dr. Gisbert Wüstholz and PD Dr. Clemens Fuchs.

In a first phase of our research project we shall study two types of problems. The first problem circles around the so-called Andre-Oort conjecture. This conjecture is located at the borderline between number theory and arithmetic algebraic geometry. We have been continuously studying various aspects of this question in the past which is documented in recent publications. One of the motivations for our studies is that there is a close connection to transcendence theory. This theory originates in the classification of real and complex numbers such as rational numbers versus irrational numbers, algebraic versus non-algebraic numbers where a real or complex number is called algebraic if it is a root of a polynomial with integral coefficients. Transcendence theory deals with non-algebraic, also called transcendental numbers. They were first mentioned by Euler, as it seems. Most numbers are transcendental but it is almost impossible to verify the transcendence of any particular given number. Coming back to the Andre-Oort conjecture it seems that two young researchers, Yafaev and Klingler, have reduced in a not yet published paper the conjecture to an even more famous and more difficult conjecture in analytic number theory. This conjecture, the Riemann hypothesis, has been open since almost 150 years and there is no hope that we shall see a proof in the near future. There is one very simple case in which the Andre-Oort conjecture has been proved by Andre himself unconditionally. The proof relies on class field theory, algebraic geometry and on a result in transcendence theory. This is our starting point. In an ambitious PhD project a very talented graduate student tries to extend the existing proof to a more general situation and to exhaust the method. As a first step a conjecture of Wuestholz in transcendence theory which generalizes a theorem of Masser and which is used in Andre's proof has to be proved. The methods needed for the transcendence part of the project are available. It is clear that the remaining part can be done subject to a number of technical difficulties. In the last three decades another system of numbers, the so-called p-adic numbers, have been studied very intensively in various parts of mathematics. They are defined for each prime number p and they are particularly useful for arithmetic studies. Also here the classification system for numbers apply and one can speak of transcendental p-adic numbers. In the second part of the research project another graduate student started to work on the analytic subgroup theorem, the most powerful existing theorem in transcendence theory. The theorem gives in a very systematic and conceptual way a large class of transcendental numbers. The goal of the project is to obtain the p-adic analogue of the analytic subgroup theorem and to deduce new classes of transcendental numbers. In the framework of the present research project there are at the moment four further ongoing PhD projects. However so far they are not financed within this research project. Further PhD projects are expected.

Projective Stacks:

Organizer: Prof. Dr. Andrew Kresch.

Algebraic varieties are the solution sets to systems of polynomial equations. An important case is that of homogeneous polynomial equations, defining projective algebraic varieties. Algebraic stacks are more general objects, not so readily encoded by means of equations. This project seeks to identify and study algebraic stacks which could be called "projective" and use the findings about algebraic stacks to address classical problems. Classically one knows that space can be extended by adding "points at infinity". Then, for instance, we may assert that parallel lines will intersect at a point at infinity. With algebraic stacks, point are endowed with the extra information of a stabilizer group. A typical geometric question about projective stacks could be, given a stack for which we have a good understanding of the points in ordinary space, can we understand the stabilizer groups at the points at infinity? The questions become more subtle and the answers more interesting in situations that are far away from classical geometry, for instance when working over a base field of positive characteristic, or in arithmetic geometry (that is, over the base ring of integers).

Diophantine and Algebraic Geometry:

Organizers: Prof. Dr. Gisbert Wüstholz and Prof. Dr. Brent Doran.

In this project we study classical algebro-geometric problems. We have two different aspects in mind. One part deals with geometric problems which come up in the classification of algebraic varieties and in birational geometry. The main tools is the motivic homotopy theory of Morel and Voevodsky. Another part is a PhD project in diophantine geometry. Here techniques from projective algebraic geometry, arithmetic intersection theory and diophantine approximations have to be combined to attack an old problem of Baker and Coates on effective bounds for the height of integral points on general hyperelliptic curves.

Cluster Categories:

Organizer: Prof. Dr. Karin Baur.

This project investigates new geometrical models for orbit categories of bounded derived categories such as cluster categories. The cluster category associated to a path algebra A is defined as the orbit category under a certain autoequivalence of the bounded derived category of A-modules. Cluster categories can be modelled using triangulations of regular polygons. Similarly, m-cluster categories can be modelled by dividing polygons into smaller polygons. Cluster categories have been introduced because of their combinatorial similarity with cluster algebras. As such they provide an example of a categorification, i.e. of the process of associating a category to an algebraic object. The questions arising here naturally are: What is the dictionary between the properties of the original (algebraic) object and the properties of the category and of the associated functors? How do results from the first setting translate to the categorical setting?

Local and globald equidisbribution for arithmetic objects:

Organizer: Prof. Dr. Emmanual Kowalski

The research goals of the proposal concern some important aspects of analytic number theory where the notion of equidistribution is of high importance, and where important links with probability theory arise. Whereas many existing works can be interpreted in this manner, they do not usually highlight this in a systematic manner. However, developing more thoroughly the general framework seems to be likely to be very useful, in particular to understand in greater depth some cases where, in the current state of knowledge, only conjectures supported by numerical or heuristic arguments exist. The project proposes to look at these types of problems in the following situations: •In the setting of the conjectures concerning the distribution of values of L-functions, based on theoretical, heuristic and numerical evidence, where Random Matrix Theory plays an important role, many fundamental problems remain unsolved, but the recent introduction of the notion of ``mod-Gaussian'' and ``mod-Poisson'' convergence of sequences of random variables suggests a number of new relations with probability, and (at least in the setting of function fields) hopes for new approaches. •Quite general problems have been treated more systematically recently by generalizing the sieve methods of classical analytic number theory, but the applications of these techniques are far from being exhausted. The links with counting problems of hyperbolic type, recently investigated by many authors, and with random walks on discrete groups, will be looked-at in much greater detail. •A very natural question of analytic number theory, which has not yet been investigated in depth, is to consider families of (global) L-functions, say associated with automorphic representations of GL(n), and ask about the distribution, either for a fixed prime or uniformly, of the local components of the representations in the spectrum of the local p-adic group. This question seems, however, to be likely to be of great importance in understanding higher rank L-functions. •One can define various invariants of finite groups using ideas of probabilistic group theory, and their distribution in the case of Galois groups, and in particular for families of number fields, becomes a problem intricately related with sieve techniques and questions about L-functions.

Jean-Pierre Wintenberger (Strasbourg), 16.02.2009-30.05.2009

Carlo Gasbarri (Università di Roma "Tor Vergata"), 02.04.2009-03.04.2009

Valentin Blomer (Toronto), 10.05.2009-15.05.2009

Bas Edixhoven (Leiden), 10.05.2009-15.05.2009

Hélène Esnault (Duisburg-Essen), 10.05.2009-15.05.2009

Jay Jorgensen (CCNY), 10.05.2009-15.05.2009

Chandrashekhar Khare (UCLA), 10.05.2009-15.05.2009

Bruno Klingler (Princeton), 10.05.2009-15.05.2009

Maxim Kontsevich (IHES), 10.05.2009-15.05.2009

Jürg Kramer (Berlin), 10.05.2009-15.05.2009

Kenneth A. Ribet (Berkeley), 10.05.2009-15.05.2009

Yuri Tschinkel (NYU), 10.05.2009-15.05.2009

Eckhard Viehweg (Duisburg-Essen), 10.05.2009-15.05.2009

Andrei Yafaev (UCL), 10.05.2009-15.05.2009

Yuri Zarhin (Penn State), 02.08.2009-15.08.2009

Michael Stoll (Bayreuth), 12.08.2009-16.08.2009

Sergej Gorchinskiy (Russian Academy of Science, Moscow), 01.09.2009-28.02.2010

Umberto Zannier (SNS Pisa), 02.06.2009-07.06.2009 and 01.10.2009-28.10.2009

Tzanko Matev (Bayreuth), 25.10.2009-31.10.2009

Hironori Shiga (Waseda University Tokyo), 07.01.2010-15.01.2010

Florian Luca (UNAM), 01.03.2010-09.03.2010

Shanta Laishram (IIT Dehli), 19.05.2010-01.07.2010

N. Saradha (TIFR), 20.05.2010-06.06.2010

Speakers at the FIM-Workshop "Rational Points - Theory & Experiment", 25.05.2010-29.05.2010

Laurent Berger (Lyon), 18.07.2010-23.07.2010

Giovanni di Matteo (Lyon), 18.07.2010-23.07.2010

Sergey Gorchinskiy (Moscow), 15.07.2010-27.07.2010

Sergey Rybakov (Moscow), 15.07.2010-27.07.2010

Anna-Maria von Pippich (Basel), 23.09.2010-24.09.2010

Patrick Tuen Wai Ng (Hong Kong), 18.10.2010-25.10.2010

Speakers at the FIM-Workshop "Exponential sums over finite fields and applications", 01.11.2010-05.11.2010

Alain Togbe (Purdue North Central), 02.11.2010-05.11.2010

Winfried Kohnen (Heidelberg), 29.04.2011

Kunrui Yu (Hong Kong University of Science and Technology), 04.05.2011-04.06.2011

Paula Tretkoff (Texas A&M University), 09.05.2011-10.05.2011

Solomon Friedberg (Boston College), 14.05.2011-21.05.2011

Sergey Gorchinskiy (Moscow), 09.07.2011-20.07.2011

Annette Huber-Klawitter (Freiburg), 16.07.2011-19.07.2011

Stefan Müller-Stach (Mainz), 16.07.2011-19.07.2011

Sergey Rybakov (Moscow), 13.07.2011-19.07.2011

Sonia Samol (Mainz), 13.07.2011-19.07.2011

Konrad Völkel (Freiburg), 13.07.2011-19.07.2011

Jonas von Wangenheim (Freiburg), 13.07.2011-19.07.2011

Thomas Weißschuh (Mainz), 13.07.2011-19.07.2011

Peter Wieland (Freiburg), 13.07.2011-19.07.2011

Cormac O'Sullivan (Bronx Community College / CUNY Graduate Center), 25.09.-01.10.2011

Ngô Bao Châu (University of Chicago), 25.10.-27.10.2011

Stephen Kudla (University of Toronto), 25.10.-27.10.2011

Guy Henniart (Université Paris-Sud 11), 25.10.-27.10.2011

Philipp Habegger (University of Frankfurt), 02.12.2011

Lars Kühne (SNS Pisa), 31.01.2012

Winfried Khonen (Heidelberg), 28.03.2012

Umberto Zannier (SNS Pisa), 06.03.2012-09.03.2012

Jeffrey Hoffstein (Brown University), 29.03.2012

Sergey Gorchinskiy (Moscow), 10.04.2012-14.04.2012

Javier Fresan (Paris), 13.09.2013

Sergey Gorchinskiy (Moscow), 28.09.2012

Konrad Völkel (Universität Freiburg), 07.12.2012

Ishai Dan-Cohen (Universität Duisburg-Essen), 15.11.2012

Annette Werner (Göttingen), 23.11.2012

Konrad Völkel (Freiburg), 06.12.2012

Clemens Fuchs (Salzburg), 17.02.2013-19.02.2013

Marc Levine (Duisburg-Essen), 23.05.2013-07.06.2013

Lars Kühne (SNS Pisa), 24.05.2013-07.06.2013

Rafael von Kanel (Paris), 24.05.2013-07.06.2013

Ngaiming Mok (Hong Kong), 24.05.2013-07.06.2013

Ioulia Beloshapka (Moscow), 04.07.2013-13.07.2013

Clemens Fuchs (Salzburg), 19.08.2013-22.08.2013

For further publications and (in particular) preprints see the personal web pages of the participating members of the ProDoc. •A. Momot: On the classification of complex tori arising from real Abelian surfaces, Abh. Math. Sem. Univ. Hambg. 79 (2009), 283-298. •C. Fuchs, T.N. Shorey: Divisibility properties of generalized Laguerre polynomials, Indag. Math. (N.S.) 20 (2009), 217-231. •C. Fuchs: Polynomial-exponential equations involving multi-recurrences, Stud. Sci. Math. Hungar. 46 (2009), 377-398. •C. Fuchs, R.F. Tichy, V. Ziegler: On quantitative aspects of the unit sum number problem, Arch. Math. 93 (2009), 259-268. •R. von Känel: An effective proof of the hyperelliptic Shafarevich conjecture and applications, PhD thesis, ETH Zurich, 2010. •T. Preu: Transcendental Brauer-Manin obstruction for a diagonal quartic surface, PhD thesis, Univ. of Zurich, 2010. •C. Fuchs, R. von Känel, G. Wüstholz: An effective Shafarevich theorem for elliptic curves, Acta Arith. 148 (2011), 189-203. •C. Fuchs, A. Pethö: Composite rational functions having a bounded number of zeros and poles, Proc. AMS 139 (2011), 31-38. •C. Fuchs: Angle trisection with Origami and related topics, Elem. Math. 66 (2011), 121-136. •M. Wang: Rational points and transcendental points, PhD thesis, ETH Zurich, 2011. •L. Kühne: An effective result of André-Oort type, PhD thesis, ETH Zurich, 2012. •A. Momot: Density of rational points on commutative algebraic groups and small transendence degree, PhD thesis, ETH Zurich, 2012. •C. Fuchs, U. Zannier: Composite rational functions expressible with few terms, J. Eur. Math. Soc. 14 (2012), 175-208. •A. Dujella, C. Fuchs: On a problem of Diophantus for rationals, J. Number Theory 132 (2012), 2075-2083. •H. Pham: New progress in p-adic transcendence theory, PhD thesis, ETH Zurich, 2013. •L. Kühne: An effective result of André-Oort type, Ann. Math. (2) 176 (2012), 651-671. •C. Fuchs, T.N. Shorey: Divisibility properties of hypergeometric polynomials, J. Comb. Number Theory 4 (2012), 1-10. •J. Jermann: Interlacing property of the zeros of j_n(tau), Proc. AMS 140 (2013), 3385-3396. •T.W. Ng, M. Wang: Ritt's theory on the unit disk, Forum Math. 25 (2013), 821-851. •T. Preu: Example of a transcendental 3-torsion Brauer-Manin obstruction on a diagonal quartic surface, LMS Lecture Note Series "Torsors, étale homotopy and applications to rational points", to appear. •J. Skowera: Bialynicki-Birula decomposition of Deligne Mumford stacks, Proc. AMS 141 (2013), 1933-1937. •Y.F. Bilu, C. Fuchs, F. Luca, Á. Pintér: Combinatorial Diophantine equations and a refinement of a theorem on separated variables equations, Publ. Math. Debrecen 82 (2013), 219-254. •G. Wüstholz: Leibniz' conjecture, periods & motives, Colloquium De Giorgi 2009 (Edizioni della Normale, 2012 edition (May 28, 2012). •M. Wang, G. Wüstholz: Meromorphic Maps on Riemann Surfaces and Transcendence, Sovremennye Problemy Matematiki 17 (2013), 113-134. •M. Walter, B. Doran, D. Gross, M. Christandl: Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information, Science 340 (2013), 1205-1208. •J. Ayoub, S. Zucker: Relative Artin motives and the reductive Borel-Serre compactification of a locally symmetric variety, Invent. Math. 188 (2012), 277–427. •J. Ayoub: Le carré du foncteur de dualité est monoïdal, Comm. Algebra 39 (2011), 1528–1535. •J. Ayoub: The n-motivic t-structures for n=0, 1 and 2, Adv. Math. 226 (2011), 111–138. •J. Ayoub: Note sur les opérations de Grothendieck et la réalisation de Betti, J. Inst. Math. Jussieu 9 (2010), 225–263. •J. Ayoub, L. Barbieri-Viale: 1-motivic sheaves and the Albanese functor, J. Pure Appl. Algebra 213 (2009), 809–839. •W. Duke, Ö. Imamoglu, Á. Tóth: Real quadratic analogs of traces of singular moduli, Int. Math. Res. Not. IMRN 2011, no. 13, 3082–3094. •W. Duke, Ö. Imamoglu, Á. Tóth: Cycle integrals of the j-function and mock modular forms, Ann. of Math. (2) 173 (2011), no. 2, 947–981. •W. Duke, Ö. Imamoglu, Á. Tóth: Rational period functions and cycle integrals, Abh. Math. Semin. Univ. Hambg. 80 (2010), no. 2, 255–264. •Ö. Imamoglu, N. Raulf: On the behaviour of eigenvalues of Hecke operators, Math. Res. Lett. 17 (2010), no. 1, 51–67. •Ö. Imamoglu, C. O'Sullivan: Parabolic, hyperbolic and elliptic Poincaré series, Acta Arith. 139 (2009), no. 3, 199–228. •&OUml;. Imamoglu, Y. Martin: On characteristic twists of multiple Dirichlet series associated to Siegel cusp forms, Math. Z. 263 (2009), no. 2, 345–368. •J. B. Conrey, D.W. Farmer> Ö. Imamoglu: Palindromic random trigonometric polynomials, Proc. Amer. Math. Soc. 137 (2009), no. 5, 1835–1839. •A. Kresch: Flattening stratification and the stack of partial stabilizations of prestable curves, Bull. Lond. Math. Soc. 45 (2013), no. 1, 93–102. •B. Hassett, A. Kresch, Y. Tschinkel> Effective computation of Picard groups and Brauer-Manin obstructions of degree two K3 surfaces over number fields, Rend. Circ. Mat. 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30.05.2013: Prof. Ngaiming Mok (The University of Hong Kong) Holomorphicisometries on bounded domains

23.05.2013: Prof. Marc Levine (Universität Duisburg-Essen) An introduction to motivic homotopy theory

16.05.2013: Dr. Rafael von Känel (Institut des Hautes Études Scientifiques, I.H.É.S.) Discriminants and small points of curves

25.04.2013: Sam Molcho (Brown University) Localization for log stable maps

18.03.2013-23.03.2013: Equidistribution in Number Theory and Dynamics

07.12.2012: Konrad Völkel (Universität Freiburg) Matsumoto's Theorem in Motivic Homotopy Theory

15.11.2012: Ishai Dan-Cohen (Universität Duisburg-Essen) Explicit Chabauty-Kim theory for the thrice punctured line in depth two

01.11.2012: Jonathan Skowera (UZH) Decompositions and integral cycles of algebraic stacks

25.10.2012: Lars Kühne (ETHZ) Linear independence results for odd zeta values

18.10.2012: Roland Paulin (ETHZ) Criteria for linear independence

29.03.2012: Jeffrey Hoffstein (Brown University) Multiple Dirichlet Day Dreams

08.03.2012: Umberto Zannier (SNS Pisa) Sharpening 'Manin-Mumford' for certain algebraic groups of dimension 2

10.11.2011: Roland Paulin (ETH Zürich) Minimal degree of morphisms between curves

26.10.2011: Heinz-Hopf Symposium in HG D7.2: Ngô Bao Châu (University of Chicago) at 11 am: Abelian fibration associated with the geometric side of the trace formula, Stephen Kudla (University of Toronto) at 3 pm: Modular generating series for arithmetic special cycles, Guy Henniart (Université Paris-Sud 11) at 4 pm: Modular Langlands correspondence: new avatars

29.09.2011: Cormac O'Sullivan (Bronx Community College / CUNY Graduate Center) Taylor coefficients of modular forms

09.06.2011: Martin Gallauer (UZH) Preparation for Alpbach III: proof that standard cohomology theories obey axioms, proof of theorem of de Rahm

07.06.2011 from 15:15-17:00 in HG G 19.1: Mario Huicochea, Hiep Pham Duc (ETHZ) Preparation for Alpbach II: axiomatic theory of (co-)homology theories on smooth manifolds, introduction of some standard (co-)homology theories on smooth manifolds

26.05.2011: Bledar Fazlija (ETHZ) Preparation for Alpbach I: integration of forms over cycles on smooth manifolds, theorem of Stokes, basics on homological algebra, integration of cohomology classes against homology classes

19.05.2011: Solomon Friedberg (Boston College) 15:15-16:00: Metaplectic Eisenstein Series and Multiple Dirichlet Series. Abstract: In this hour I give an introduction to metaplectic Eisenstein series and multiple Dirichlet series. No prior background concerning these topics will be assumed. 16:15-17:00: Ice Models and Automorphic Forms. Abstract: In this hour I show how ice models from statistical mechanics can be used to model automorphic forms and also multiple Dirichlet series that are related to metaplectic Eisenstein series. Once again, the relevant concepts will be described from first principles.

10.05.2011 from 17:15-18:15 in HG G 43 (HWZ): Paula Tretkoff (Texas A&M University) An Introduction to the Analytic Subgroup Theorem and its Applications (part II)

09.05.2011 from 17:15-18:15 in HG G 43 (HWZ): Paula Tretkoff (Texas A&M University) An Introduction to the Analytic Subgroup Theorem and its Applications (part I)

07.05.2011 from 11:00-12:00 in GR A3 32 at EPFL: Paula Tretkoff (Texas A&M University) Variations of Hodge Structure and the Analytic Subgroup Theorem. This first talk of the Minicourse is part of the ETH Number Theory Days 2011 (for more information see here).

07.04.2011: Martin Gallauer (Uni Zürich) Lefschetz-Verdier trace formula and a generalization of a theorem of Fujiwara

31.03.2011: Gergely Berczi (University of Oxford) Recent progress on the Green-Griffiths-Lang conjecture

10.03.2011: Lisa Lamberti (ETH Zurich) Cluster categories and their geometrical model

03.03.2011: Rafael von Känel (ETH Zurich) On the Modular Degree Conjecture

24.02.2011: Mingxi Wang (ETH Zurich) Dynamical Mordell-Lang for the polydisk

16.12.2010: Jörg Jahnel (Universität Siegen) K3 surfaces and their Picard groups

09.12.2010: Thomas Preu (Uni Zürich) The Brauer-Manin Obstruction

25.11.2010: Noah Giansiracusa (Brown University) Conformal blocks and rational normal curves

04.11.2010: Patrik Hubschmid (ETH Zurich) The André-Oort Conjecture for Drinfeld moduli spaces

14.10.2010: Gyula Karolyi (Eötvös University, Budapest / EPFL) On the Combinatorial Nullstellensatz and its applications (part II)

07.10.2010: Gyula Karolyi (Eötvös University, Budapest / EPFL) On the Combinatorial Nullstellensatz and its applications (part I)

23.09.2010: Anna von Pippich (Basel) Elliptic Eisenstein series

03.06.2010: Dzmitry Doryn (Essen) Cohomology of graph hypersurfaces and counting of points

06.05.2010 Jun Yu (ETH Zürich): On the dimension data problem (Summary of the talk), Rafael von Känel (ETH Zürich): An effective Shafarevich theorem for elliptic curves

29.04.2010 Paul Ziegler (ETH Zürich) Classification of F-Zips

13.04.2010: Heinrich Massold (Zürich) Transcendence degrees and algebraic approximation

25.03.2010: Clemens Fuchs (ETH Zürich) On decomposable lacunary rational functions (part III)

18.03.2010: Clemens Fuchs (ETH Zürich) On decomposable lacunary rational functions (part II)

11.03.2010: Charles Doran (University of Alberta, Edmonton) Normal forms for Lattice Polarized K3 Surfaces and the Kuga-Satake Hodge Conjecture

04.03.2010: Clemens Fuchs (ETH Zürich) On decomposable lacunary rational functions (part I)

14.01.2010: Hironori Shiga (Waseda University Tokyo) Period Differential Equations for Some Families of K3 Surfaces in Connection with the Hilbert Modular Group for Q(Sqrt[5]) (Prof. Shiga's script for the talk is available)

10.12.2009: Fritz Hörmann (ETH Zürich) Arithmetic and geometric volume of Shimura varieties of orthogonal type (part II)

03.12.2009: Fritz Hörmann (ETH Zürich) Arithmetic and geometric volume of Shimura varieties of orthogonal type (part I)

26.11.2009: Daniel Haase (ETH Zürich) Arithmetic Group Determinants (Slides for the talk)

19.11.2009: Maria Petkova (ETH Zürich) Ball Quotient Curves and Quaternion Algebras

12.11.2009: Simon Pepin-Lehalleur (Université Paris 13) Triangulated categories of motives and compactifications of Shimura varieties

29.10.2009: Tzanko Matev (Bayreuth) The p-adic analytic subgroup theorem

26.10.2009: Umberto Zannier (SNS Pisa) Some problems of integral points on varieties over function fields (part IV) (exceptional time and place: the talk takes place on monday in room HG G19.2 at 15-17h).

22.10.2009: Umberto Zannier (SNS Pisa) Some problems of integral points on varieties over function fields (part III)

15.10.2009: Umberto Zannier (SNS Pisa) Some problems of integral points on varieties over function fields (part II)

08.10.2009: Umberto Zannier (SNS Pisa) Some problems of integral points on varieties over function fields (part I)

24.09.2009 Alena Pirutka (ENS/Paris 11) R-equivalence on low degree complete intersections and rationally simply connected varieties

07.05.2009: Utsav Choudhury (Uni Zürich) Rational connectivity and A1-connectivity

23.04.2009 Mingxi Wang (ETH) Meromorphic maps on Riemann surfaces and transcendence

02.04.2009 Carlo Gasbarri (Univesità di Roma "Tor Vergata") Transcendence and Nevanlinna theory

26.03.2009 René Birkner (FU Berlin) An introduction to toric Hilbert schemes

19.03.2009 Jean-Pierre Wintenberger (University of Strasbourg) Construction of the Galois representation associated to a weight 2 modular form (part IV)

12.03.2009 Jean-Pierre Wintenberger (University of Strasbourg) Construction of the Galois representation associated to a weight 2 modular form (part III)

05.03.2009 Jean-Pierre Wintenberger (University of Strasbourg) Construction of the Galois representation associated to a weight 2 modular form (part II)

26.02.2009 Jean-Pierre Wintenberger (University of Strasbourg) Construction of the Galois representation associated to a weight 2 modular form (part I)

(Notes (updated 07.05.2009) from Prof. Wintenberger are available)

Aleksander Momot: Über eine Variante der Schanuel'schen Vermutung für Funktionenkörper: Formulierung der Schanuel'schen Vermutung und Konsequenzen, Freitag, 03. November 2006 um 11:10 Uhr

Aleksander Momot: Über eine Variante der Schanuel'schen Vermutung für Funktionenkörper: Beweisskizze und Beweis 1. Teil, Freitag, 06. November 2006 um 16:15 Uhr

Walter Gubler (Universität Dortmund): Berkovich Räume und tropische analytische Geometrie: Teil 1 (Minikurs im Rahmen der Zurich Graduate School of Mathematics), Montag, 13. November 2006 von 16:15 - 17:30 Uhr, HG G 19.2

Walter Gubler (Universität Dortmund): Berkovich Räume und tropische analytische Geometrie: Teil 2 (Minikurs im Rahmen der Zurich Graduate School of Mathematics), Dienstag, 14. November 2006 von 15:15 - 16:30 Uhr, HG G 19.2

Aleksander Momot: Über eine Variante der Schanuel'schen Vermutung für Funktionenkörper: Beweis des Hauptresultates, Montag, 20. November 2006 um 17:15 Uhr

Winfried Kohnen (Universität Heidelberg): Sign changes of Fourier coefficients and Hecke eigenvalues of cusp forms (Vortrag im Rahmen des Zahlentheorie Seminars), Montag, 27. November 2006 um 16:15 Uhr, HG G 26.1

Aleksander Momot: Über eine Variante der Schanuel'schen Vermutung für Funktionenkörper: Beweis des Hauptresultates II, Montag, 04. Dezember 2006 um 16:00 Uhr

Aleksander Momot: Über eine Variante der Schanuel'schen Vermutung für Funktionenkörper: Beweis des Hauptresultates III, Montag, 11. Dezember 2006 um 16:15 Uhr

Gisbert Wüstholz: A (Wüstholz-style) proof of the Theorem of Lindemann, Monday, 08th of January 2007 at 16.15pm

Gisbert Wüstholz: A (Wüstholz-style) proof of the Theorem of Lindemann. II, Monday, 15th of January 2007 at 16.15pm

Gisbert Wüstholz: A (Wüstholz-style) proof of the Theorem of Lindemann. III. Into the Proof, Monday, 22th of January 2007 at 16.15pm

Gisbert Wüstholz: A (Wüstholz-style) proof of the Theorem of Lindemann. IV. Proof, Thursday, 08th of February 2007 at 14.15pm, HWZ (HG G 43)

Gisbert Wüstholz: A (Wüstholz-style) proof of the Theorem of Lindemann. V. Proof, Monday, 12th of February 2007 at 16.15pm, HWZ (HG G 43)

Gisbert Wüstholz: A (Wüstholz-style) proof of the Theorem of Lindemann. VI. Proof, Tuesday, 06th of March 2007 at 14.15pm, HWZ (HG G 43)

Gisbert Wüstholz: A (Wüstholz-style) proof of the Theorem of Lindemann. VII. QED, Wednesday, 07th of March 2007 at 11.10pm, HWZ (HG G 43)

Clemens Fuchs: Integral points on certain algebraic varieties, Thursday, 05th of April 2007 at 15.15pm, HG F 26.3

Clemens Fuchs: Integral points on certain algebraic varieties. II. Preliminaries and first reductions, Thursday, 26th of April 2007 at 15.15pm, HG F 26.3

Clemens Fuchs: Integral points on certain algebraic varieties. III. Filtration and properties, Thursday, 03rd of May 2007 at 15.15pm, HG F 26.3

Clemens Fuchs: Integral points on certain algebraic varieties. IV. Diophantine approximation part, Thursday, 10th of May 2007 at 15.15pm, HG F 26.3

Clemens Fuchs: Integral points on certain algebraic varieties. V. Other results and conjectures, Thursday, 24th of May 2007 at 15.15pm, HG F 26.3

Clemens Fuchs: Schlechte und gute Nachrichten für Herrn Hilbert, Tuesday, 19th of June 2007 at 17:15pm, HG D 5.2

Patrik Hubschmid: Definition and examples of general l-adic representations, Thursday, 30th of August 2007 at 13.30pm, HG G 19.1

Patrik Hubschmid: l-adic representations of number fields, Thursday, 30th of August 2007 at 15.30pm, HG G 19.1

Tobias Hahn: Equidistribution and L-functions, Part I, Friday, 31st of August 2007 at 13.30pm, HG G 19.1

Tobias Hahn: Equidistribution and L-functions, Part II, Friday, 31st of August 2007 at 15.30pm, HG G 19.1

Impressum 21.03.2016