## Math Calendar

Friday, February 22, 2019

15:00-17:00

HFG 610

Friday Fish

Luca Accornero - Universal bundles I - classification theorem and examples

see description

In this talk we are going to start studying universal principal G-bundles for topological groups, whose base spaces exhibit as ordinary cohomology the equivariant cohomology of the point. We will prove the classification theorem for principal G-bundles: this states that a principal G-bundle with contractible total space is universal. Then we will provide a bunch of examples, focusing especially on the group U(n). The existence problem is postponed to the next talk.

Monday, February 25, 2019

13:00-15:00

Duistermaat

Tuesday, February 26, 2019

16:00-17:00

HFG 611

Utrecht Geometry Center Seminar

Elba García Failde (CEA Saclay) - Simple maps, Hurwitz numbers and topological recursion

see description

In this talk, we call ordinary maps a certain type of graphs embedded on surfaces, in contrast to fully simple maps, which we introduce as maps with non-intersecting disjoint boundaries. It is well-known that the generating series of ordinary maps satisfy a universal recursive procedure, called topological recursion (TR). We propose a combinatorial interpretation of the important and still mysterious symplectic transformation which exchanges $x$ and $y$ in the initial data of the TR (the spectral curve). We give elegant formulas for the disk and cylinder topologies which recover relations already known in the context of free probability. For genus zero we provide an enumerative geometric interpretation of the so-called higher order free cumulants, which suggests the possibility of a general theory of approximate higher order free cumulants taking into account the higher genus amplitudes. We also give a universal relation between fully simple and ordinary maps involving double monotone Hurwitz numbers, which relies on a matrix model interpretation of fully simple maps via the formal hermitian matrix model with external field. In particular, we obtain an ELSV-like formula for double strictly monotone Hurwitz numbers with ramification profile $(2,\ldots,2)$ over $0$ and arbitrary one over $\infty$.

17:00-22:00

HFG 610

We will go over some of the themes that form the backbone of Contact and Symplectic Topology. We will do this Russian style: the seminar starts at 5 and it is open ended (and at some point we will order dinner). Additionally, it will be extremely informal and it will probably devolve into a discussion among the participants. The topics to be covered are: Floer theory, Contact and Symplectic flexibility, and generating functions.

Friday, March 1, 2019

10:30-13:00

HFG 610

Monday, March 4, 2019

13:00-15:00

Duistermaat

13:00-15:00

HFG 610

Tuesday, March 5, 2019

16:00-17:00

HFG 611

Utrecht Geometry Center Seminar

Rahul Pandharipande (ETH Zuerich) - Enumerative geometry and the holomorphic anomaly equation

see description

Abstract: I will give a (gentle) introduction to the role of the holomorphic anomaly equation in curve counting problems starting with maps to elliptic curves, proceeding to local toric geometries, and concluding with the famous quintic 3-fold. Though I will discuss joint work with Hyenho Lho, much of what I will say is work of others (Pixton, Oberdieck-Pixton, Chen-Guo-Janda-Ruan, Jun Li and collaborators).

Thursday, March 7, 2019

15:30-16:30

MIN 2.01

The Utrecht Mathematical Colloquium

Rahul Pandharipande (ETH Zürich) - From Abel-Jacobi to the double ramification cycle and beyond

see description

Abstract:

A basic question in the theory of algebraic curves is whether a

divisor represents the zeros and poles of a rational function.

An explicit solution in terms of periods was given by the work of Abel

and Jacobi in the 19th century. In the past few years, a different

approach to the question has been pursued: what is the class

in the moduli of pointed curves of the locus of such divisors? I will

explain the answer in Gromov-Witten theory given by Pixton's formula

for the double ramification cycle. More recently, the subject has been

developing in several new directions which I will present. My work

here is joint with F. Janda, A. Pixton, and D. Zvonkine.

A basic question in the theory of algebraic curves is whether a

divisor represents the zeros and poles of a rational function.

An explicit solution in terms of periods was given by the work of Abel

and Jacobi in the 19th century. In the past few years, a different

approach to the question has been pursued: what is the class

in the moduli of pointed curves of the locus of such divisors? I will

explain the answer in Gromov-Witten theory given by Pixton's formula

for the double ramification cycle. More recently, the subject has been

developing in several new directions which I will present. My work

here is joint with F. Janda, A. Pixton, and D. Zvonkine.

16:00-17:00

Utrecht

Complex Systems Seminar

Caterina Zeppieri (Universität Münster) - Homogenization of high-contrast Mumford-Shah energies , HFG 611

see description

Title: Homogenization of high-contrast Mumford-Shah energies

Abstract: We prove a homogenization result for Mumford-Shah-type functionals with degenerate periodic coefficients. These kind of functionals can be used to model the energy of a brittle periodic material whose constituents have very different mechanical properties. We show that the high-contrast behavior of the constituents leads, in the homogenized limit, to the emergence of nonstandard macroscopic effects.

Abstract: We prove a homogenization result for Mumford-Shah-type functionals with degenerate periodic coefficients. These kind of functionals can be used to model the energy of a brittle periodic material whose constituents have very different mechanical properties. We show that the high-contrast behavior of the constituents leads, in the homogenized limit, to the emergence of nonstandard macroscopic effects.

Monday, March 11, 2019

13:00-15:00

HFG 610

13:00-15:00

Duistermaat

Tuesday, March 12, 2019

16:00-17:00

HFG 611

Utrecht Geometry Center Seminar

Lóránt Szegedy (MPIM) - Topological field theory on r-spin surfaces and the Arf invariant

see description

After a brief introduction to r-spin structures on surfaces we present a state-sum construction of r-spin TFTs based on a combinatorial model of r-spin surfaces. We give an example of such a TFT which computes the Arf invariant for even values of r. Using the combinatorial model and this TFT we calculate diffeomorphism classes of r-spin surfaces with parametrized boundary. This is joint work with Ingo Runkel.

Thursday, March 14, 2019

Friday, March 15, 2019

11:00-12:00

We prove an analogue of the Prime Number Theorem for short intervals on a smooth proper curve of arbitrary genus over a finite field. Our main result gives a uniform asymptotic count of those rational functions, inside short intervals defined by a very ample effective divisor E, whose principal divisors are prime away from E.In this talk, I will discuss the setting and definitions we use in order to make sense of such count, and will give a rough sketch of the proof. This is a joint work with Tyler Foster.

13:15-14:15

(2) Francesca Balestrieri (MPIM Bonn) - Arithmetic of zero-cycles on products of Kummer varieties and K3 surfaces

see description

Abstract: The following is joint work with Rachel Newton. In the spirit of work by Yongqi Liang, we relate the arithmetic of rational points to that of zero-cycles for the class of Kummer varieties over number fields. In particular, if X is any Kummer variety over a number field k, we show that if the Brauer-Manin obstruction is the only obstruction to the existence of rational points on X over all finite extensions of k, then the Brauer-Manin obstruction is the only obstruction to the existence of a zero-cycle of any odd degree on X. Building on this result and on some other recent results by Ieronymou, Skorobogatov and Zarhin, we further prove a similar Liang-type result for products of Kummer varieties and K3 surfaces over k.

14:15-15:15

To reduce to resolving Cohen-Macaulay singularities, Faltings initiated the program of "Macaulayfying" a given Noetherian scheme X. Under various assumptions Faltings, Brodmann, and Kawasaki built the sought Cohen-Macaulay modifications without preserving the locus where X is already Cohen-Macaulay. We will discuss an approach that overcomes this difficulty and hence completes Faltings' program.

15:30-16:30

Abstract:

Given a tower of Shimura varieties (where the level at a fixed prime p grows) one may ask whether one can equip the inverse limit with a geometric structure.

As I will explain in the talk, this is possible in many cases. The geometric structure is that of a perfectoid space.

I will then show you the impact of this results by explaining some applications.

Given a tower of Shimura varieties (where the level at a fixed prime p grows) one may ask whether one can equip the inverse limit with a geometric structure.

As I will explain in the talk, this is possible in many cases. The geometric structure is that of a perfectoid space.

I will then show you the impact of this results by explaining some applications.

Monday, March 18, 2019

13:00-15:00

Duistermaat

13:00-15:00

HFG 610

Tuesday, March 19, 2019

16:00-17:00

HFG 611

Thursday, March 21, 2019

16:00-17:00

Utrecht

Monday, March 25, 2019

13:00-15:00

HFG 610

13:00-15:00

Duistermaat

Tuesday, March 26, 2019

16:00-17:00

HFG 611

Utrecht Geometry Center Seminar

Christoph Winges (MPIM Bonn) - Coarse homology theories and assembly maps

see description

Coarse homology theories provide an analog of homology theories which is adapted to the purposes of large-scale geometry. I will survey how they can be utilised to provide concrete models of assembly maps. As time allows, I will also explain an axiomatic framework which facilitates proofs of split-injectivity results for various assembly maps. This recovers known results eg for the algebraic K-theory of discrete group rings, but also accomodates invariants such as A-theory. Joint work with Ulrich Bunke, Alexander Engel and Daniel Kasprowski.

Thursday, March 28, 2019

Monday, April 1, 2019

13:00-15:00

Duistermaat

13:00-15:00

HFG 610

Tuesday, April 2, 2019

16:00-17:00

HFG 611

Monday, April 8, 2019

13:00-15:00

HFG 610

13:00-15:00

Duistermaat

Tuesday, April 9, 2019

Thursday, April 11, 2019

Monday, April 15, 2019

13:00-15:00

HFG 610

Tuesday, April 16, 2019

16:00-17:00

HFG 611

Tuesday, April 23, 2019

16:00-17:00

HFG 611

Monday, April 29, 2019

13:00-15:00

HFG 610

Tuesday, April 30, 2019

Thursday, May 2, 2019

16:00-17:00

Utrecht

Monday, May 6, 2019

13:00-15:00

HFG 610

Tuesday, May 7, 2019

16:00-17:00

HFG 611

Monday, May 13, 2019

13:00-15:00

HFG 610

Tuesday, May 14, 2019

16:00-17:00

HFG 611

Monday, May 20, 2019

13:00-15:00

HFG 610

Tuesday, May 21, 2019

16:00-17:00

HFG 611

Thursday, May 23, 2019

Tuesday, May 28, 2019

16:00-17:00

HFG 611

Tuesday, June 4, 2019

16:00-17:00

HFG 611

Thursday, June 6, 2019

16:00-17:00

Utrecht

Tuesday, June 11, 2019

Tuesday, June 18, 2019

16:00-17:00

HFG 611

Tuesday, June 25, 2019

Tuesday, July 2, 2019

Tuesday, July 9, 2019

Tuesday, July 16, 2019

Tuesday, July 23, 2019

Tuesday, July 30, 2019

Tuesday, August 6, 2019

Tuesday, August 13, 2019

Tuesday, August 20, 2019