Past Junior Geometry and Topology Seminar

7 March 2019
16:00
Moritz Oliver Meisel
Abstract

In this talk, I will sketch a geometrically flavoured proof of the 
Madsen-Weiss theorem based on work by Eliashberg-Galatius-Mishachev.
In order to prove the triviality of appropriate relative bordism groups, 
in a first step a variant of the wrinkling theorem shows
that one can reduce to consider fold maps (with additional structure). 
In a subsequent step, a geometric version of the Harer stability
theorem is used to get rid of the folds via surgery. I will focus on 
this second step.

  • Junior Geometry and Topology Seminar
28 February 2019
16:00
Filip Zivanovic
Abstract

Standard representation theory transforms groups=algebra into vector spaces = (linear) algebra. The modern approach, geometric representation theory constructs geometric objects from algebra and captures various algebraic representations through geometric gadgets/invariants on these objects. This field started with celebrated Borel-Weil-Bott and Beilinson-Bernstein theorems but equally is in rapid expansion nowadays. I will start from the very beginnings of this field and try to get to the recent developments (time permitting).

  • Junior Geometry and Topology Seminar
14 February 2019
16:00
Maxence Mayrand
Abstract

I will describe a family of 2d TQFTs, due to Moore-Tachikawa, which take values in a category whose objects are Lie groups and whose morphisms are holomorphic symplectic varieties. They link many interesting aspects of geometry, such as moduli spaces of solutions to Nahm equations, hyperkähler reduction, and geometric invariant theory.

  • Junior Geometry and Topology Seminar
7 February 2019
16:00
Mehdi Yazdi
Abstract

I will give an overview of the Nielsen-Thurston theory of the mapping class group and its connection to hyperbolic geometry and dynamics. Time permitting, I will discuss the surface entropy conjecture and a theorem of Hamenstadt on entropies of `generic' elements of the mapping class group. No prior knowledge of the concepts involved is required.

  • Junior Geometry and Topology Seminar
31 January 2019
16:00
Andreas Bode
Abstract

Since differentiation generally lowers exponents, it is straightforward that the space of Laurent polynomials $\mathbb{C}[x, x^{-1}]$ is a finitely generated module over the ring of differential operators $\mathbb{C}[x, \mathrm{d}/\mathrm{d}x]$. This innocent looking fact has been vastly generalized to a statement about holonomic D-modules, using the beautiful theory of b-functions (or Bernstein—Sato polynomials). I will give an overview of the classical theory before discussing some recent developments concerning a $p$-adic analytic analogue, which is joint work with Thomas Bitoun.

  • Junior Geometry and Topology Seminar
24 January 2019
16:00
Thomas Prince
Abstract

The Strominger-Yau-Zaslow (SYZ) conjecture postulates that mirror dual Calabi-Yau manifolds carry dual special Lagrangian fibrations. Within the study of Mirror Symmetry the SYZ conjecture has provided a particularly fruitful point of convergence of ideas from Riemannian, Symplectic, Tropical, and Algebraic geometry over the last twenty years. I will attempt to provide a brief overview of this aspect of Mirror Symmetry.

  • Junior Geometry and Topology Seminar
17 January 2019
16:00
Dogancan Karabaş
Abstract

It is shown by Kashiwara and Schapira (1980s) that for every constructible sheaf on a smooth manifold, one can construct a closed conic Lagrangian subset of its cotangent bundle, called the microsupport of the sheaf. This eventually led to the equivalence of the category of constructible sheaves on a manifold and the Fukaya category of its cotangent bundle by the work of Nadler and Zaslow (2006), and Ganatra, Pardon, and Shende (2018) for partially wrapped Fukaya categories. One can try to generalise this and conjecture that Fukaya category of a Weinstein manifold can be given by constructible (microlocal) sheaves associated to its skeleton. In this talk, I will explain these concepts and confirm the conjecture for a family of Weinstein manifolds which are certain quotients of A_n-Milnor fibres. I will outline the computation of their wrapped Fukaya categories and microlocal sheaves on their skeleta, called pinwheels.

  • Junior Geometry and Topology Seminar
29 November 2018
16:00
Eric Schlarmann
Abstract

The usual finite dimensional Grassmannians are well known to be classifying spaces for vector bundles. It is maybe a less known fact that one has certain natural connections on the Stiefel bundles over them, which also have a universality property. I will show how these connections are constructed and explain how this viewpoint can be used to rediscover Chern-Weil theory. Finally, we will see how a certain stabilized version of this, called the restricted Grassmannian, admits a similar construction, which can be used to show that it is a smooth classifying space for differential K-theory.

  • Junior Geometry and Topology Seminar

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