Past Forthcoming Seminars

25 May 2018
16:00
Claudia Scheimbauer and Alberto Paganini
Abstract

Claudia Scheimbauer

Title: Quantum field theory meets higher categories

Abstract: Studying physics has always been a driving force in the development of many beautiful pieces of mathematics in many different areas. In the last century, quantum field theory has been a central such force and there have been several fundamentally different approaches using and developing vastly different mathematical tools. One of them, Atiyah and Segal's axiomatic approach to topological and conformal quantum field theories, provides a beautiful link between the geometry of "spacetimes” (mathematically described as cobordisms) and algebraic structures. Combining this approach with the physical notion of "locality" led to the introduction of the language of higher categories into the topic. The Cobordism Hypothesis classifies "fully local" topological field theories and gives us a recipe to construct examples thereof by checking certain algebraic conditions generalizing the existence of the dual of a vector space. I will give an introduction to the topic and very briefly mention on my own work on these "extended" topological field theories.

Alberto Paganini

Title: Shape Optimization with Finite Elements

Abstract: Shape optimization means looking for a domain that minimizes a target cost functional. Such problems are commonly solved iteratively by constructing a minimizing sequence of domains. Often, the target cost functional depends on the solution to a boundary value problem stated on the domain to be optimized. This introduces the difficulty of solving a boundary value problem on a domain that changes at each iteration. I will suggest how to address this issue using finite elements and conclude with an application from optics.

25 May 2018
14:00
Professor Stephen Gourley
Abstract

I will discuss some properties of delay differential equations in which the delay is not prescribed a-priori but is determined from a threshold condition. Sometimes the delay depends on the solution of the differential equation and its history. A scenario giving rise to a threshold type delay is that larval insects sometimes experience halting or slowing down of development, known as diapause, perhaps as a consequence of intra-specific competition among larvae at higher densities. Threshold delays can result in population dynamical models having some unusual properties, for example, if the model has an Allee effect then diapause may cause extinction in some parameter regimes even where the initial population is high.

Please  note that this talk is only suitable for Mathematicians.

  • Mathematical Biology and Ecology Seminar
25 May 2018
12:00
Florian Pausinger
Abstract

Persistent homology is an algebraic tool for quantifying topological features of shapes and functions, which has recently found wide applications in data and shape analysis. In the first and introductory part of this talk I recall the underlying ideas and basic concepts of this very active field of research. In the second part, I plan to sketch a concrete application of this concept to digital image processing. 

  • Applied Algebra and Topology
24 May 2018
16:00
to
17:30
Michael Kupper
Abstract

We present a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network with smooth objective function. We present numerical examples from optimal transport, and bounds on the distribution of a sum of dependent random variables. As an application we focus on the problem of risk aggregation under model uncertainty. The talk is based on joint work with Stephan Eckstein and Mathias Pohl.

  • Mathematical and Computational Finance Seminar
24 May 2018
16:00
William Petersen
Abstract

The Witten-Reshetikhin-Turaev invariant Z(X,K) of a closed oriented three-manifold X containing a knot K, was originally introduced by Witten in order to extend the Jones polynomial of knots  in terms of Chern-Simons theory. Classically, the Jones polynomial is defined for a knot inside the three-sphere in  a combinatorial manner. In Witten's approach, the Jones polynomial J(K) emerge as the expectation value of a certain observable in Chern-Simons theory, which makes sense when K is embedded in any closed oriented three-manifold X. Moreover; he proposed that these invariants should be extendable to so-called topological quantum field theories (TQFT's). There is a catch; Witten's ideas relied on Feynman path integrals, which made them unrigorous from a mathematical point of view. However; TQFT's extending the Jones polynomial were subsequently constructed mathematically through combinatorial means by Reshetikhin and Turaev. In this talk, I shall expand slightly on the historical motivation of WRT invariants, introduce the formalism of TQFT's, and present some of the open problems concerning WRT invariants. The guiding motif will be the analogy between TQFT and quantum field theory.

  • Junior Geometry and Topology Seminar
24 May 2018
16:00
to
17:30
Frederic Dias
Abstract

Statements in media about record wave heights being measured are more and more common, the latest being about a record wave of almost 24m in the Southern Ocean on 9 May 2018. We will review some of these wave measurements and the various techniques to measure waves. Then we will explain the various mechanisms that can produce extreme waves both in wave tanks and in the ocean. We will conclude by providing the mechanism that, we believe, explains some of the famous extreme waves. Note that extreme waves are not necessarily rogue waves and that rogue waves are not necessarily extreme waves.

  • Industrial and Applied Mathematics Seminar
24 May 2018
16:00
Edgar Assing
Abstract

We will briefly revisit Voronoi summation in its classical form and mention some of its many applications in number theory. We will then show how to use the global Whittaker model to create Voronoi type formulae. This new approach allows for a wide range of weights and twists. In the end we give some applications to the subconvexity problem of degree two $L$-functions. 

  • Number Theory Seminar

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