### Conferences - Seminars

27FEB

10:15-11:15
CIB - BI A0 448

## "Syzygies of curves"

The study of the equations defining projective varieties, and the relations (i.e. syzygies) amongst them has an old and venerable history. First considered around 1850 in the work of Sylvester, the computation of syzygies has remains a central topic in algebra to this day. Much later on, it was realised that syzygies arise naturally in ...
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By

**Assistant Prof. Michael Kemeny***(Stanford University**)*
27FEB

14:15-15:15
CIB - BI A0 448

## "Vector bundles on algebraic varieties"

The study of vector bundles on algebraic varieties is a classical topic at the intersection of geometry and commutative algebra. In its algebraic form it is the study of finitely generated projective modules over commutative rings. There are many long-standing conjectures and open questions about algebraic vector bundles, such as: is every topological vector bundle ...
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By

**Dr. Marc Hoyois***(Massachusetts Institute of Technology**)*
27FEB

14:15-15:30
GC A1 416

## Generalizations of the Rips filtration for quasi-metric spaces with corresponding stability results

Rips filtrations over a finite metric space and their corresponding persistent homology are prominent methods in Topological Data Analysis to summarize the ``shape'' of data. For finite metric space X and distance r the traditional Rips complex with parameter r is the flag complex whose vertices are the points in X and whose edges are ...
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By Kate Turner (EPFL)

28FEB

09:15-10:15
CIB - BI A0 448

## "Generalised negative curvature and the geometry of groups"

Geometric group theory involves the study of groups as geometric objects, often via their (well-behaved) actions on (tractable) spaces, from which information about the group -- algebraic, geometric, algorithmic, etc. -- can be decocted. A major theme is that this method is particularly powerful when the spaces in question exhibit features of negative or nonpositive ...
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By

**Dr. Mark Hagen***(University of Cambridge**)*
28FEB

11:15-12:15
CIB - BI A0 448

## "Lattice actions on manifolds and recent progress in the Zimmer program"

The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular, on manifolds whose dimension is below the dimension of all algebraic examples, Zimmer’s ...
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By

**L. E. Dickson Instructor Dr. Aaron Brown***(University of Chicago**)*
28FEB

14:15-15:15
CIB - BI A0 448

## "The structure of transport equations and the Vlasov-Poisson system"

The transport equation describes the evolution of a distribution of particles moving along the flow of a prescribed smooth vector field. An accurate description of its solutions, even when the smoothness assumption is dropped, is motivated by several applications, among which the study of kinetic equations such as the Vlasov-Poisson system. Given a vector field ...
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By

**Dr. Maria Colombo***(ETHZ - ITS**)*
01MAR

09:15-10:15
CIB - BI A0 448

## "Dynamic beyond criticality"

I will present in this talk some probabilistics model studied in physics, which are ill-posed from an analytic point of view due to a dramatic lack of regularity and where the classical tools of stochastic analysis fail to be applied. The aim of this talk is to present an approach to overcome this kind of ...
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By

**Dr. Khalil Chouk***(Technische Universität Berlin**)*
01MAR

11:15-12:15
CIB - BI A0 448

## "Regularity of free boundaries in obstacle problems"

We present a brief overview of the regularity theory for free boundaries in obstacle problems. We describe how a monotonicity formula of Almgren plays a central role in the study of the regularity of the free boundary in some of these problems. Finally, we explain new strategies which we have recently developed to deal with ...
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By

**R. H. Bing Instructor Dr. Xavier Ros-Oton***(University of Texas ...*
01MAR

14:15-15:15
CIB - BI A0 448

## "Beyond positivity"

The Hard Lefschetz Theorem's importance extends far beyond algebraic geometry. In particular, many deceptively simple combinatorial conjectures seem depend on this mysterious theorem, but are only known to be true if the associated varieties satisfy the Lefschetz theorem by virtue of the Kaehler package. For instance, Gruenbaum conjectured that for any simplicial d-complex X embedded ...
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By

**Dr. Karim Adiprasito***(Hebrew University Jerusalem**)*
01MAR

15:30-16:30
CH B3 31

## (Twisted) Derived category of Enriques Surfaces in characteristic 2

Abstract: We show that the (twisted) derived category recognizes the three types of Enriques surfaces in characteristic 2.
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By Sofia Tirabassi (University of Bergen)

01MAR

16:30-17:30
INF 213

## Finitude des mesures de Gibbs sur les variétés non compactes à courbure négative.

Nous établissons un critère d'ergodicité ainsi que trois critères de finitude pour les mesures de Gibbs sur les variétés non compactes à courbure négative pincée. Ces critères sont inspirés des critères de Sarig de récurrence et récurrence positive pour les sous-décalage sur un alphabet infini, mais leur preuve ne repose pas sur le codage. En ...
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By Vincent Pit

02MAR

10:15-11:15
CIB - BI A0 448

## "CM-theoretic Aspects of the Birch and Swinnerton-Dyer Conjecture and Curve-Based Cryptography"

The theory of complex multiplication (CM theory) has found numerous applications in both modern number theory, arithmetic geometry and mathematical cryptology. In this talk, I will give a basic background on the BSD conjecture and outline the main ideas of the recent proof of the conjectural formula for elliptic curves of analytic rank 1. I ...
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By

**Prof. Dimitar Jetchev***(EPFL**)*
02MAR

15:15-16:15
CO 015

## Around Vinogradov's theorem

Vinogradov in 1937 proved the ternary version of the Goldbach conjecture, that every large odd integer can be written as a sum of three primes. In this talk, I will start with a historical account on some related problems and the underlying methods, and then describe a few new results related to the ternary Goldbach ...
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By Fernando Shao (University of Oxford)

03MAR

11:00-12:00
Campus Biotech, B1.06 (lakeside)

## An exposition of memory-augmented artificial neural networks

Biologically inspired machine learning algorithms known as artificial neural networks have been around since the 1950s, but have rapidly gained popularity over the last decade due to increases in computational power and the sheer volume of data available. The simplest forms of these, feed-forward neural networks, have two major shortcomings: they require input of fixed ...
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By William Mycroft (Sheffield)