You are invited to take part in the:

**Mathematical-Physics Seminar**

January 23rd, 2020

**Registration is closed.**

**Schedule**:

10:20-10:45: Gathering, coffee & light refreshments on the 8th floor

10:45-11:45: **Uzy Smilansky (Weizmann)**

11:45-12:45: Lunch on the 8th floor

12:45-13:45: **Barry Simon (Caltech)**

13:45-14:00: break

14:00-15:00: **Percy Deift (NYU)**

15:00-15:30: Coffe & light refreshments on the 8th floor

15:30-16:30: **David Jerison (MIT)**

All lectures will take place at the Auditorium 232, Amado Mathematics Building.

Coffee & light refreshments will be given in the Faculty lounge on the 8th floor.

**Titles and abstracts:**

**Uzy Smilansky (Weizmann)** – *Two trace formulae for Hermitian matrices*

**Abstract**: Trace formulae are one of the most important tools in a large number of fields ranging from quantum chaos via spectral geometry, graphs and number theory.

Here, we present two rather unconventional trace formulae for Hermitian matrices which generalize previously derived expressions for quantum and combinatorial graphs.

**Barry Simon (Caltech) – Reflection Positivity as a Tool in the Theory of Phase Transitions**

**Abstract**: In recognition of the 100^{th} anniversary of the Ising model, I describe the use of reflection positivity in the theory of phase transitions. I will especially focus on presenting the method of Infrared Bounds.

**Percy Deift (NYU) – Universality aspects of numerical computation with random data**

**Abstract**: The speaker will describe ongoing work on universality for standard numerical algorithms with random data. The speaker will

focus on recent work concerning the solution of random linear systems and creating keys for cyber algorithms.

This work is joint with various authors: C.Pfrang, G.Menon, S.Olver, S.Miller and mostly T. Trogdon

**David Jerison (MIT) – Global solutions and rigidity**

**Abstract**: We will explain how complex analysis and differential geometry, in particular as developed for minimal surface theory, can be used to characterize global solutions and prove rigidity and regularity results for free boundaries. This gives further insights into the missing ingredients that will be needed to understand level sets of eigenfunctions.