Matematiikan ja systeemianalyysin laitos


Esitelmiä, seminaareja ja väitöksiä

* Seuraavan viikon tapahtumat merkitty tähdellä

Katherine Maxwell (Kavli IPMU)
Superstring measure extended to supergrassmannian space
* Today * Thursday 20 June 2024,   10:15,   M3 (M234)
I will describe an extension of the integration measure for calculating scattering amplitudes in (super)string theory to a large (super)grassmannian space, known as the super Sato grassmannian. In comparison to bosonic string theory, superstring theory provides some simplifications in the properties of the integration measure, which I will highlight in my talk. On the other hand, superstring theory is intrinsically related to the supermoduli space of super Riemann surfaces, which poses challenges because of the supergeometric structure. I will explain why working with supergrassmannian space could be a good solution to these problems. This is based off of joint work with Alexander Voronov.

Ryosuke Sato (Chuo University)
CAR algebras and stochastic processes on random point processes
* Tuesday 25 June 2024,   10:15,   M3 (M234)
CAR algebras are fundamental operator algebras that appear in various fields of mathematics and mathematical physics. In this talk, we will focus on its relationship to random point processes, which are mathematical descriptions of random interacting particles. In particular, after discussing the relation between quasi-free states of CAR algebras and determinantal point processes, we will investigate how the operator algebraic framework provides stochastic processes on random point processes.

Toni Annala (IAS)
Motivic homotopy theory
* Tuesday 25 June 2024,   14:15,   M3 (M234)
Cohomology theories are an integral part of modern algebraic geometry. In algebraic topology, (stable) homotopy theory provides a convenient framework to study various cohomology theories and their interrelations. In algebraic geometry, a similar role should be played by motivic homotopy theory, which strictly generalizes Grothendieck's dream of motives. In the first part of the talk, I will motivate the necessity of homotopy theory to study cohomology theories in algebraic topology and algebraic geometry. I will also introduce A^1-homotopy theory, defined by Morel and Voevodsky in the late 90s. In the second part of my talk, I will introduce the motivic stable homotopy theory, which is the subject of my long-term project with Marc Hoyois, Ryomei Iwasa, and others. The goal of this theory is to build a framework for studying all cohomology theories in algebraic geometry simultaneously. I will give some sample results, and explain what concrete consequences can be derived from our results.
Algebra & Discrete Math Seminar

Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
* Wednesday 26 June 2024,   09:00,   M3 (M234)
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