Events & Seminars

2015 Dec 22

Number theory: Alexei Entin (Stanford) "Monodromy of Hurwitz spaces and extensions of F_q(t)"

10:30am to 11:45am

Location: 

Ross Building, room 70A
Hurwitz spaces are moduli spaces for extensions of curves with prescribed ramification types. They arise naturally when enumerating extensions of global function fields and also in many other contexts. The classical Hurwitz space H_{m,n} may be viewed as a finite cover of the space of n-sets of points on P^1. We will show that this cover has a big monodromy group for n>4. This can be applied to study the statistics of extensions of F_q(t) with varying branching locus in the large q limit. Joint work with Chris Hall and Robert Guralnick.
2017 Dec 25

NG&AT: Avner Segal (UBC) "Poles of the Standard L-function and Functorial Lifts for G2"

3:00pm to 4:00pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
The functoriality conjecture is a key ingredient in the theory of automorphic forms and the Langlands program. Given two reductive groups G and H, the principle of functoriality asserts that a map r:H^->G^ between their dual complex groups should naturally give rise to a map r*:Rep(H)->Rep(G) between their automorphic representations. In this talk, I will describe the idea of functoriality, its connection to L-functions and recent work on weak functorial lifts to the exceptional group of type G_2.
2016 Mar 17

Number theory

Repeats every week every Thursday until Thu Jun 16 2016 except Thu Apr 14 2016.
12:00pm to 1:15pm

12:00pm to 1:15pm
12:00pm to 1:15pm
12:00pm to 1:15pm
12:00pm to 1:15pm
12:00pm to 1:15pm
12:00pm to 1:15pm
12:00pm to 1:15pm
12:00pm to 1:15pm
12:00pm to 1:15pm
12:00pm to 1:15pm
12:00pm to 1:15pm
12:00pm to 1:15pm

Location: 

Ross Building, room 63, Jerusalem, Israel
In his investigation of modular forms of half-integral weight, Shimura established, using Hecke theory, a family of relations between eigneforms of half-integral weight k+1/2 with a given level 4N and character chi and cusp forms of weight 2k and character chi^2. The level being subsequently determined by Niwa to be at most 2N.
2017 Feb 27

NT&AG: Stephen Lichtenbaum (Brown University), "A conjectured cohomological description of special values of zeta-functions"

2:00pm to 3:00pm

Location: 

Ross 70A
Abstract: Let X be a regular scheme, projective and flat over Spec Z. We give a conjectural formula in terms of motivic cohomology, singular cohomology and de Rham cohomology for the special value of the zeta-function of X at any rational integer. We will explain how this reduces to the standard formula for the residue of the Dedekind zeta-function at s = 1. ‏האירוע הזה כולל שיחת וידאו ב-Google Hangouts.
2017 Nov 06

NT&AG: Walter Gubler (University of Regensburg), "The non-archimedean Monge-Ampère problem"

2:00pm to 3:00pm

Location: 

Ros 70
Abstract: Calabi conjectured that the complex Monge-Ampère equation on compact Kaehler manifolds has a unique solution. This was solved by Yau in 1978. In this talk, we present a non-archimedean version on projective Berkovich spaces. In joint work with Burgos, Jell, Künnemann and Martin, we improve a result of Boucksom, Favre and Jonsson in the equicharacteristic 0 case. We give also a result in positive equicharacteristic using test ideals.
2016 Apr 21

Number Theory: Benjamin Matschke (University of Bordeaux) "A database of rational elliptic curves with given bad reduction"

2:00pm to 3:15pm

Location: 

TBA
In this talk we present a database of rational elliptic curves with good reduction outside certain finite sets of primes, including the set {2, 3, 5, 7, 11}, and all sets whose product is at most 1000. In fact this is a biproduct of a larger project, in which we construct practical algorithms to solve S-unit, Mordell, cubic Thue, cubic Thue--Mahler, as well as generalized Ramanujan--Nagell equations, and to compute S-integral points on rational elliptic curves with given Mordell--Weil basis. Our algorithms rely on new height bounds, which we obtained using the
2016 Dec 19

NT&AG: Edva Roditty-Gershon (University of Bristol), "Arithmetic statistics in function fields"

2:00pm to 3:00pm

Location: 

Manchester Building, Faculty Lounge
Abstract: In the talk I will discuss classical problems concerning the distribution of square-full numbers and their analogues over function fields. The results described are in the context of the ring Fq[T ] of polynomials over a finite field Fq of q elements, in the limit q → ∞. I will also present some recent generalization of these kind of classical problems. ‏האירוע הזה כולל שיחת וידאו ב-Google Hangouts.
2017 Jun 05

NT&AG: Simon Marshall (University of Wisconsin), "Endoscopy and cohomology growth on U(n,1) Shimura varieties"

2:00pm to 3:00pm

Location: 

Ros 70
Using the endoscopic classification of automorphic forms for unitary groups, I will prove conjecturally sharp upper bounds for the growth of Betti numbers in congruence towers of complex hyperbolic manifolds. This is joint work with Sug Woo Shin. ‏האירוע הזה כולל שיחת וידאו ב-Google Hangouts. הצטרף: https://plus.google.com/hangouts/_/calendar/ODdkc2JxNmlmbjNhZ2U0ODVvb3E3...
2016 Mar 17

Number theory

Repeats every week every Thursday until Wed Mar 16 2016 .
12:00pm to 1:15pm

Location: 

Ross Building, room 70, Jerusalem, Israel
2018 Jan 08

NT&AG: Hershy Kisilevsky (Concordia University), "Special Values of twists of Modular/Elliptic L-Functions"

2:00pm to 3:00pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
Let L(E/Q, s) be the L-function of an elliptic curve E defined over the rational field Q. We examine the central value L(E, 1, χ) of twists of L(E/Q, s) by Dirichlet characters χ. We discuss the vanishing and non-vanishing frequencies of these values as χ ranges over characters of fixed order greater than 2. We also examine thee square-free part of the algebraic part of L(E/F, 1) for abelian fields F/Q when these values are non-zero.
2017 May 29

NT&AG: Nicolas Templier (Cornell University), "Mirror symmetry for minuscule flag varieties"

2:00pm to 3:00pm

Location: 

Ros70A
We prove cases of Rietsch mirror conjecture that the quantum connection for projective homogeneous varieties is isomorphic to the pushforward D-module attached to Berenstein-Kazhdan geometric crystals. The idea is to recognize the quantum connection as Galois and the geometric crystal as automorphic. In particular we link the purity of Berenstein-Kazhdan crystals to the Ramanujan property of certain Hecke eigensheaves. The isomorphism of D-modules comes from global rigidity results where a Hecke eigenform is determined by its local ramification. We reveal
2016 Feb 15

Number theory: Andrey Levin (Moscow) "Kronecker double series at CM points and dilogarithm"

2:00pm to 3:00pm

Location: 

Ross building, 70A
This talk is in natural in the context of the Zagier conjecture. We express values of the Kronecker double series at CM points in terms of values some version (Bloch-Wigner) of dilogarithm in algebraic numbers. As zeta-function of the Hilbert class field of quadratic field can be expressed as combination of the Kronecker double series at CM points my result gives explicit form of the Zagier conjecture. My technique is rather elementary and the proof is based on the introduction some new function (elliptic (1,1)-logarithm) and comparisons with it.
2018 Jan 01

NT&AG: Efrat Bank (University of Michigan), "Correlation between primes in short intervals on curves over finite fields"

2:00pm to 3:00pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
In this talk, I present an analogue of the Hardy-Littlewood conjecture on the asymptotic distribution of prime constellations in the setting of short intervals in function fields of smooth projective curves over finite fields. I will discuss the definition of a "short interval" on a curve as an additive translation of the space of global sections of a sufficiently positive divisor E by a suitable rational function f, and show how this definition generalizes the definition of a short interval in the polynomial setting.
2016 Nov 21

NT&AG: Damaris Schindler (Utrecht University), "Systems of quadratic forms"

2:00pm to 3:00pm

Location: 

Ros Building, 70A
In this talk we discuss some aspects concerning the arithmetic of systems of quadratic forms. This includes a result on the frequency of counterexamples to the Hasse principle for del Pezzo surfaces of degree four (joint work with J. Jahnel), and a result on the representability of integers by systems of three quadratic forms (joint work with L. B. Pierce and M. M. Wood).

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