# Seminar: Basic Notions, Winter Term 2017/2018

Organisers: Constantin Eichenberg , Marco Fraccaroli , João Pedro Ramos, Catharina Stroppel

This seminar is organised by students as a BIGS event. The goal is to present topics from all areas of mathematics in an elementary and informal way. The talks should be accessible to a general mathematical audience.
Everybody (students, postdocs, faculty, guests) is welcome to attend.
Coffee, tea and cookies will be served afterwards.

For receiving updates and information on upcoming talks, you can also subscribe to our Facebook page.

The seminar will take place Wednesdays 14-16 in room 1.007.

Previous instances of this seminar:
Summer Term 2017,
Winter Term 2016/17, Summer Term 2016,
Winter Term 2015/16, Summer Term 2015,
Winter Term 2014/15, Summer Term 2014,
Winter Term 2013/14.

Date Speaker Topic
25.10.2017 Marco Fraccaroli The Erdös distinct distances problem: a geometric approach.
01.11.2017
All Saints' Day
08.11.2017
No talk.
15.11.2017
No talk.
22.11.2017
No talk due to GlobalMathNetwork.
29.11.2017 Immanuel Zachhuber Rough Paths and Singular Stochastic PDEs.
06.12.2017
No talk.
13.12.2017
No talk.
20.12.2017
No talk.
10.01.2018
No talk.
17.01.2018
No talk.
24.01.2018
No talk.
31.01.2018 David Hornshaw An introduction to non-commutative geometry.

October 25, 2017: Marco Fraccaroli

The Erdös distinct distances problem: a geometric approach.

Abstract. The Erdös distinct distances problem is one emblematic example of the many questions posed by the prolific Hungarian mathematician: simple in the statement and yet surprisingly rich and deep in the level of mathematics involved in the solution.

The question is the following:

how few distinct distances are determined by a set of N points in the plane?

A heuristic approach suggests that the simmetries of the set play an important role in minimizing the number of distinct distances determined by it.

Following the paper "On the Erdös distinct distances problem in the plane" of Guth and Katz, we will present the way to make this idea rigorous. Studying the problem in the group of rigid motions of the plane (translations and rotations), we will convert the problem to one of point-line incidences in space.

Finally, we will briefly review some of the many research directions (all still open) starting from the Erdös distinct distances problem.

November 29, 2017: Immanuel Zachhuber

Rough Paths and Singular Stochastic PDEs.

Abstract. "Rough Paths" were introduced in the '90s by Lyons to give a path-wise theory of stochastic integration. The theory was considerably reformulated and extended by Gubinelli in the early 00's in the form of "Controlled Paths", which gave a way, amongst other things, to solve some singular Stochastic PDEs. After some SSPDEs were solved using Rough Path methods, e.g. the Stochastic Burgers equation by Hairer, a major breakthrough occurred in the form of "Regularity Structures" and "Paracontrolled Distributions" which were developed in parallel by Hairer and Gubinelli/Imkeller/Perkowski respectively around 2014.

We will give a brief introduction to the topic of "Rough Paths" as well as a glimpse of "Paracontrolled Distributions". Furthermore we will discuss the scope, and limitations, of the theories. Time permitting we will apply the theory of "Paracontrolled Distributions" to a specific SSPDE to give an impression of the general method.

January 31, 2018: David Hornshaw

An introduction to non-commutative geometry..

Abstract. We give an introduction to noncommutative geometry with motivation originating in physics.

The talk has three goals: first, we establish naturality of noncommutativity. Secondly, we show that it is first and foremost a non-geometric property. Thirdly, we discuss what additionalstructure one requires in order to obtain a noncommutative geometric one by in-depth examination of the two-dimensional fuzzy torus.