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.
If you would like to give a talk please contact us. Our email address is basicnotions(at)hcm.unibonn.de.
For receiving updates and information on upcoming talks, you can also subscribe to our Facebook page.
The seminar will take place Wednesdays 1416 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  
08.11.2017  
15.11.2017  
22.11.2017  
29.11.2017  Immanuel Zachhuber  Rough Paths and Singular Stochastic PDEs. 
06.12.2017 
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 pointline incidences in space.
Finally, we will briefly review some of the many research directions (all still open) starting from the Erdös distinct distances problem.

Rough Paths and Singular Stochastic PDEs.

Abstract. "Rough Paths" were introduced in the '90s by Lyons to give a
pathwise 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.
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