Departement Mathematik

Number theory seminar

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Herbstsemester 2019

Datum / Zeit Referent:in Titel Ort
11. Oktober 2019
14:15-15:15 		Dr. Yongxiao Lin
EPF Lausanne
Details

Number Theory Seminar

Titel Applications of simple delta methods toward twists of modular forms
Referent:in, Affiliation Dr. Yongxiao Lin, EPF Lausanne
Datum, Zeit 11. Oktober 2019, 14:15-15:15
Ort HG G 43
Abstract We will explain how some simple delta symbol methods can be used to obtain non-correlation of fixed GL(2) modular forms against certain trace functions or exponential functions of oscillatory phase. In particular this gives a simple proof of a hybrid Burgess-Weyl type subconvexity for the twisted GL(2) L-functions. This talk is based on joint works with K. Aggarwal, R. Holowinsky, Z. Qi, and Q. Sun.
Applications of simple delta methods toward twists of modular formsread_more
HG G 43
18. Oktober 2019
14:15-15:15 		Prof. Dr. Silvain Rideau-Kikuchi
Université Paris-Diderot
Details

Number Theory Seminar

Titel Interpretable groups in algebraically closed valued fields
Referent:in, Affiliation Prof. Dr. Silvain Rideau-Kikuchi, Université Paris-Diderot
Datum, Zeit 18. Oktober 2019, 14:15-15:15
Ort HG G 43
Abstract (Joint with Ehud Hrushovski) The class of groups interpretable in an algebraically closed valued field K contains, among other things, algebraic groups over K, algebraic groups over its residue field k and groups interpretable in the valued group (mostly circles and lines). In this talk we will give elements of a structure theory for these groups that aims, in the spirit of the Ax-Kochen-Ersov principle, to decompose them in terms of the aforementioned classes. The subclass of, so-called « stably dominated groups »: interpretable groups whose action on its Hrushovski-Loeser space (an equivalent of the Berkovich analytificaion of varieties) has a fix point; plays a fundamental role in the structure theory. Our main result, reminiscent of semi-stable reduction, is that every commutative interpretable group has a maximal quotient internal to the valued group whose kernel is an increasing union of stably dominated subgroups. We also show that stably dominated groups are related to flat group schemes over the valuation ring.
Interpretable groups in algebraically closed valued fieldsread_more
HG G 43
* 21. Oktober 2019
14:00-15:00 		Prof. Dr. Ken Ribet
UC Berkeley
Details

Number Theory Seminar

Titel The cuspidal group and the rational torsion subgroup of the Jacobian of the modular curve X_0(N)
Referent:in, Affiliation Prof. Dr. Ken Ribet, UC Berkeley
Datum, Zeit 21. Oktober 2019, 14:00-15:00
Ort HG G 43
The cuspidal group and the rational torsion subgroup of the Jacobian of the modular curve X_0(N)
HG G 43
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Details

Number Theory Seminar

Titel Number Theory Days 2019
Referent:in, Affiliation
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Ort HG tba
Number Theory Days 2019
HG tba
1. November 2019
14:15-15:15 		Subhajit Jana
ETH Zurich, Switzerland
Details

Number Theory Seminar

Titel Analytic newvectors for $GL_n(\mathbb{R})$ and applications
Referent:in, Affiliation Subhajit Jana, ETH Zurich, Switzerland
Datum, Zeit 1. November 2019, 14:15-15:15
Ort HG G 43
Abstract We introduce a notion of a newvector at the archimedean place of the group $GL(n)$ as an analytic analogue of the classical non-archimedean newvector theory pioneered by Casselman, Jacquet--Piatetski-Shapiro--Shalika. We provide an application of these analytic newvectors in the problem of counting cuspidal automorphic representations for $PGL_n(\mathbb{Z})$ weighted by the inverse of certain $L$-value.
Analytic newvectors for $GL_n(\mathbb{R})$ and applicationsread_more
HG G 43
8. November 2019
14:15-15:15 		Prof. Dr. Fernando Rodriguez Villegas
ICTP
Details

Number Theory Seminar

Titel Independence polynomials and hypergeometric series
Referent:in, Affiliation Prof. Dr. Fernando Rodriguez Villegas, ICTP
Datum, Zeit 8. November 2019, 14:15-15:15
Ort HG G 43
Abstract Let Γ be a simple graph and I_Γ(x) its multivariate independence polynomial. The main result of this talk is the characterization of chordal graphs as the only Γ for which the power series expansion of I_Γ(x)^s is Horn hypergeometric. This is joint work with Danylo Radchenko.
Independence polynomials and hypergeometric seriesread_more
HG G 43
15. November 2019
14:15-15:15 		Prof. Dr. Paul Nelson
ETH Zurich, Switzerland
Details

Number Theory Seminar

Titel Eisenstein series and the cubic moment for PGL(2)
Referent:in, Affiliation Prof. Dr. Paul Nelson, ETH Zurich, Switzerland
Datum, Zeit 15. November 2019, 14:15-15:15
Ort HG G 43
Abstract We will discuss how to study the cubic moment of any family of automorphic L-functions on PGL(2) using regularized diagonal periods of Eisenstein series, following a strategy suggested by Michel--Venkatesh. Applications include generalizations to the setting of number fields of some results of Conrey--Iwaniec and Petrow--Young.
Eisenstein series and the cubic moment for PGL(2)read_more
HG G 43
22. November 2019
14:15-15:15 		Prof. Dr. Dimitri Wyss
EPF Lausanne
Details

Number Theory Seminar

Titel Non-Archimedean integrals on the Hitchin fibration
Referent:in, Affiliation Prof. Dr. Dimitri Wyss, EPF Lausanne
Datum, Zeit 22. November 2019, 14:15-15:15
Ort HG G 43
Abstract Non-archimedean or p-adic integration is an analytic tool to study rational points of algebraic varieties over finite fields. Dener-Loser and Batyrev have realized that this can be used in some cases to study the topology of complex algebraic varieties. We apply this idea to the moduli spaces of G-Higgs bundles and show in particular, that for a pair of Langlands dual groups their corresponding moduli spaces have the same non-archimedean volume. This leads to a new proof of the geometric stabilization theorem, a key ingredient in Ngô's proof of the fundamental lemma in the Langlands program. This is joint work with Michael Groechenig and Paul Ziegler.
Non-Archimedean integrals on the Hitchin fibrationread_more
HG G 43
29. November 2019
14:15-15:15 		Dr. Oleksiy Klurman
KTH
Details

Number Theory Seminar

Titel Boundary-adapted arithmetic random waves and spectral semi-correlations
Referent:in, Affiliation Dr. Oleksiy Klurman, KTH
Datum, Zeit 29. November 2019, 14:15-15:15
Ort HG G 43
Abstract In this talk, we test M. Berry's ansatz on nodal deficiency in presence of boundary. The square billiard is studied, where the high spectral degeneracies allow for the introduction of a Gaussian ensemble of random Laplace eigenfunctions ("boundary-adapted arithmetic random waves"). As a result of a precise asymptotic analysis, two terms in the asymptotic expansion of the expected nodal length are derived, in the high energy limit along a generic sequence of energy levels. In particular, we shall focus on a number-theoretic aspect of this problem, describing the techniques introduced by E. Bombieri and J. Bourgain to study additive equations for integral points on the circles. This is based on a joint work with V. Cammarota and I. Wigman.
Boundary-adapted arithmetic random waves and spectral semi-correlationsread_more
HG G 43
6. Dezember 2019
14:15-15:15 		Prof. Dr. Uri Onn
Australian National University
Details

Number Theory Seminar

Titel Representation growth of arithmetic lattices
Referent:in, Affiliation Prof. Dr. Uri Onn, Australian National University
Datum, Zeit 6. Dezember 2019, 14:15-15:15
Ort HG G 43
Abstract Let G be a group and let r(n,G) denote the number of equivalence classes of n-dimensional complex irreducible representations of G. Representation growth is a branch of asymptotic group theory that studies the asymptotic and arithmetic properties of the sequences (r(n,G)). In 2008 Larsen and Lubotzky conjectured that all irreducible lattices in a high rank semisimple Lie group have the same degree of polynomial representation growth. In this talk I will explain the conjecture and describe the ideas around the proof of a variant of the conjecture: if the lattices have polynomial representation growth (which is known to be true in most cases) then they have the same degree of polynomial growth. This is a joint work with Nir Avni, Benjamin Klopsch and Christopher Voll.
Representation growth of arithmetic latticesread_more
HG G 43
13. Dezember 2019
14:15-15:15 		Prof. Dr. Ambrus Pal
Imperial College
Details

Number Theory Seminar

Titel Special values of L-functions and the rigid analytical regulator of Mumford curves in positive characteristic (joint with Oli Gregory)
Referent:in, Affiliation Prof. Dr. Ambrus Pal, Imperial College
Datum, Zeit 13. Dezember 2019, 14:15-15:15
Ort HG G 43
Abstract Let X be a smooth, projective, geometrically irreducible curve over a function field F of transcendence degree over over a finite field. Assume that X is a Mumford curve over a completion K of F. We relate the rigid analytic regulator of X over K to special values of L-functions attached to X under the assumption that a special case of Parshin's conjecture holds for a regular projective model of X. Our tools include the de Rham-Witt complex, Rülling’s residues, and the Katz conjecture, proved by Emerton and Kisin.
Special values of L-functions and the rigid analytical regulator of Mumford curves in positive characteristic (joint with Oli Gregory)read_more
HG G 43

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