## Math Calendar

Friday, April 20, 2018

11:00-13:00

HFG 610

In this talk we will explore three important classes of EDSs: the aim is on one side to highlight their connections with PDEs and on the other to lay the groundwork for the study of prolongations.

An independence conditions for an EDS consists of a class of differential forms not belonging to the ideal; every PDE can be written as an EDS with a natural independence condition, corresponding to the choice of the independent variables.

Involutivity is the existence of an ordinary integral element at any point: for real-analytic EDSs, this is precisely the hypothesis to apply Cartan-Kähler and get integral manifolds through every point. We will give the examples of an involutive EDS (the one given by an involutive distribution) and a non-involutive one (having an extra "hidden" integrability condition).

Last, all EDSs induced by PDEs turn out to be examples of Pfaffian systems with a certain "linearity" property (with an unfortunate choice of name); indeed, we conclude reviewing the definition of Pfaffian bundle (the "geometric structure" encoding a PDE on a jet bundle) and showing that it also induces a linear Pfaffian system with an independence condition.

An independence conditions for an EDS consists of a class of differential forms not belonging to the ideal; every PDE can be written as an EDS with a natural independence condition, corresponding to the choice of the independent variables.

Involutivity is the existence of an ordinary integral element at any point: for real-analytic EDSs, this is precisely the hypothesis to apply Cartan-Kähler and get integral manifolds through every point. We will give the examples of an involutive EDS (the one given by an involutive distribution) and a non-involutive one (having an extra "hidden" integrability condition).

Last, all EDSs induced by PDEs turn out to be examples of Pfaffian systems with a certain "linearity" property (with an unfortunate choice of name); indeed, we conclude reviewing the definition of Pfaffian bundle (the "geometric structure" encoding a PDE on a jet bundle) and showing that it also induces a linear Pfaffian system with an independence condition.

14:00-16:00

HFG 610

Last week we saw how singular intersections can locally be described by affine derived schemes. After a brief recollection, I will discuss how singular quotients can be described by derived stacks. In the first half of the talk, I will describe stacks in the smooth setting, in terms of Lie groupoids. In the second half, I will give an analogous description of derived stacks and discuss the cotangent bundle of a derived stack.

Monday, April 23, 2018

15:00-17:00

HFG 610

Tuesday, April 24, 2018

13:15-15:00

HFG 610

16:00-17:00

HFG 611

Utrecht Geometry Center Seminar

Jaclyn Lang (MPIM Bonn) - Images of domain-valued GL2-type Galois representations

see description

Abstract: There is a general philosophy that the image of a Galois representation should be as large as possible, subject to the symmetries of the geometric object from which it arose. This can be seen in Serre's open image theorem for non-CM elliptic curves, Ribet and Momose's work on Galois representations attached to modular forms, and recent work of the speaker and Conti, Iovita, Tilouine on Galois representations attached to Hida and Coleman families of modular forms. Recently, Bellaiche developed a way to measure the image of an arbitrary Galois representation taking values in GL2 of a local ring A. Under the assumptions that A is a domain and the residual representation is not too degenerate, we explain how the symmetries of such a representation are reflected in its image. This is joint work with Andrea Conti and Anna Medvedovsky.

Monday, April 30, 2018

15:00-17:00

HFG 610

Tuesday, May 1, 2018

13:15-15:00

HFG 610

Monday, May 7, 2018

15:00-17:00

HFG 610

Tuesday, May 8, 2018

Monday, May 14, 2018

15:00-17:00

HFG 610

Tuesday, May 15, 2018

13:15-15:00

HFG 610

16:00-17:00

HFG 611

Thursday, May 17, 2018

16:00-17:00

HFG 611

Tuesday, May 22, 2018

16:00-17:00

HFG 611

Monday, May 28, 2018

Tuesday, May 29, 2018

16:00-17:00

HFG 611

Monday, June 4, 2018

Tuesday, June 5, 2018

16:00-17:00

HFG 611

Monday, June 11, 2018

Tuesday, June 12, 2018

Thursday, June 14, 2018

15:30-16:30

Ruppert ROOD

Monday, June 18, 2018

Tuesday, June 19, 2018

Thursday, June 21, 2018

16:00-17:00

Extra Number Theory Talk

Mikhail Borovoi (Tel Aviv University) - Cayley groups, MIN 2.06

see description

Abstract

I will start the talk from the classical "Cayley transform" for the special orthogonal group SO(n) defined by Arthur Cayley in 1846. A connected linear algebraic group G over C is called a *Cayley group* if it admits a *Cayley map*, that is, a G-equivariant birational isomorphism between the group variety G and its Lie algebra Lie(G). For example, SO(n) is a Cayley group. A linear algebraic group G is called *stably Cayley* if G x S is Cayley for some torus S. I will consider semisimple algebraic groups, in particular, simple algebraic groups. I will describe classification of Cayley simple groups and of stably Cayley semisimple groups. (Based on joint works with Boris Kunyavskii and others.)

Monday, June 25, 2018

Tuesday, June 26, 2018

16:00-17:00

HFG 611

Tuesday, July 3, 2018

Tuesday, July 10, 2018

Tuesday, July 17, 2018

Tuesday, July 24, 2018

Tuesday, July 31, 2018

Tuesday, August 7, 2018

Tuesday, August 14, 2018

Tuesday, August 21, 2018

Tuesday, August 28, 2018

Tuesday, September 4, 2018

Tuesday, September 11, 2018

Tuesday, September 18, 2018

Tuesday, September 25, 2018

Tuesday, October 2, 2018

Tuesday, October 9, 2018

Tuesday, October 16, 2018