# Events Winter Semester 2019/2020

##### PhD Seminar and PhD Day

We are happy to introduce you to the talks of our PhD seminar and PhD day!

Next PhD Seminar: 29.01.2019, 16:00-16:45. Enrico Reiß (Universität Potsdam)

• Title: Weyl Asymptotics for Difference Operators and Statistical Mechanics
• Abstract: The physically motivated quantization procedure generates an operator (the so-called pseudo-differential operator, PDO) from a function on the phase space $$\mathbb{R}^n \times \mathbb{R}^n$$ (the so-called symbol). In the semiclassical limit, where the Planck's constant is supposed to be a small parameter, one finds conditions allowing to approximate the number of eigenvalues of an elliptic PDO by the phase space volume of the corresponding symbol (known under Weyl asymptotics).
A family of difference operators for functions on an $\epsilon$-scaled lattice can be interpreted as discrete versions of PDOs if the corresponding symbols are supposed to be periodic with respect to the momentum component. Adapting the techniques from the continuous setting to our discrete case, we can derive similar Weyl asymptotics for difference operators.
The discrete theory is motivated by statistical mechanics: Consider for example the Curie-Weiss model where N particles interact. The magnetization of the system takes values in a scaled lattice with lattice spacing 1/N. Time evolution in this model can be described by a reversible Markov chain in discrete time, with transition matrix P. Then 1-P  is analog to a self-adjoint infinitesimal generator, or in physical language to the Hamilton operator of the system. After h-transform with respect to the reversible measure one has transformed to a space with counting measure. Hilbert space theory on this space can be written down by use of Fourier transform, which allows to realize these Hamilton operators as discrete pseudo-differential operators.

# New here?

If you recently started your Ph.D. at our Institute, please do the following:

• Add yourself to our PhD student mailing list mathe-doc. (To do this write a request to Mr. Dathe {dathe[at]uni-potsdam.de} or to one of the PhD representatives.)
• Participate in our one-per-semester PhD day and in our monthly PhD seminar! Find out what other PhD students are working on or give a talk yourself!

# Ph.D.Representatives

The current Ph.D. representatives are Florian Fischer and Undine Falkenhagen.

What do we do?

• Come to us with any questions, concerns or problems regarding your PhD studies.
• We represent the group of PhD students in mathematics in the Institutsrat.
• We organize the PhD day and PhD seminar together with the organizing committee.
• We organize regular meetings for PhD students.

If you are interested in our events, or if you want to organize one yourself, get on our mailing list "mathe-doc"and/or contact us.