# CMS[ Edit ]

*Announcement:*

You are invited to a:

** Distinguished Lecture Series by**

**Prof. Sergei Tabachnikov**

**(Pennsylvania State University)**

**Title: **Frieze patterns. Cross-ratio dynamics on ideal polygons.

**Abstract: **

In the first lecture I shall describe basic properties of frieze patterns. These are are beautiful combinatorial objects, introduced by Coxeter in the early 1970s. He was about 30 years ahead of time: only in this century, frieze patterns have become a popular object of study, in particular, due to their relation with the emerging theory of cluster algebras and to the theory of completely integrable systems. I shall prove the theorem of Conway and Coxeter that relates arithmetical frieze patterns with triangulations of polygons. There is an intimate, and somewhat unexpected, relation between three objects: frieze patterns, 2nd order linear difference equations, and polygons in the projective line (or ideal polygons in the hyperbolic plane).

**1st lecture**: Monday, January 6, 2020 at 15:30

**2nd lecture**: Wednesday, January 8, 2020 at 15:30

**3rd lecture**: Thursday, January 9, 2020 at 15:30

All lectures will be in Amado 232.

Light refreshments will be given in the faculty lounge on the 8th floor.

*Announcement:*

You are invited to a:

** Distinguished Lecture Series by**

**Prof. Sergei Tabachnikov**

**Pennsylvania State University **

**Title: ***Frieze patterns. Cross-ratio dynamics on ideal polygons.*

**Abstract: **In the next lectures I shall outline some recent work on frieze patterns, including their relation with the Virasoro algebra. Then I shall present cross-ratio dynamics on ideal polygons. Define a relation between labeled ideal polygons in the hyperbolic 3-space by requiring that the complex distances (a combination of the distance and the angle) between their respective sides equal a constant; the constant is a parameter of the relation. This gives a 1-parameter family of maps on the moduli space of ideal polygons in the hyperbolic space (or, in its real version, in the hyperbolic plane). I shall discuss complete integrability of this family of maps and related topics, including a continuous version of this relation that is intimately related with the Korteweg-de Vries equation.

**1st lecture**: Monday, January 6, 2020 at 15:30

**2nd lecture**: Wednesday, January 8, 2020 at 15:30

**3rd lecture**: Thursday, January 9, 2020 at 15:30

All lectures will be in Amado 232.

Light refreshments will be given in the faculty lounge on the 8th floor.

*Announcement:*

You are invited to a:

** Distinguished Lecture Series by**

**Prof. Sergei Tabachnikov**

**Pennsylvania State University **

**Title: ***Frieze patterns. Cross-ratio dynamics on ideal polygons.*

**Abstract: **In the next lectures I shall outline some recent work on frieze patterns, including their relation with the Virasoro algebra. Then I shall present cross-ratio dynamics on ideal polygons. Define a relation between labeled ideal polygons in the hyperbolic 3-space by requiring that the complex distances (a combination of the distance and the angle) between their respective sides equal a constant; the constant is a parameter of the relation. This gives a 1-parameter family of maps on the moduli space of ideal polygons in the hyperbolic space (or, in its real version, in the hyperbolic plane). I shall discuss complete integrability of this family of maps and related topics, including a continuous version of this relation that is intimately related with the Korteweg-de Vries equation.

**1st lecture**: Monday, January 6, 2020 at 15:30

**2nd lecture**: Wednesday, January 8, 2020 at 15:30

**3rd lecture**: Thursday, January 9, 2020 at 15:30

All lectures will be in Amado 232.

Light refreshments will be given in the faculty lounge on the 8th floor.

*Announcement:*

You are invited to a:

** Distinguished Lecture Series by**

**Prof. David Jerison (MIT)**

Abstract:

In Lecture 1 we will begin by describing the Hot Spots Conjecture of J. Rauch.This question is an essential test of our understanding of the shapes of level sets of thesimplest eigenfunctions. We will then relate our question to a variety of others about levelsets and other kinds of interfaces - free boundaries, minimal surfaces, isoperimetric surfaces - as well as the KLS Hyperplane Conjecture in high dimensional convex analysis.

**1st lecture**: Monday, January 20, 2020 at 15:30

**2nd lecture**: Wednesday, January 22, 2020 at 15:30

**3rd lecture**: Thursday, January 23, 2020 at 15:30

All lectures will be in Amado 232.

Light refreshments will be given in the faculty lounge on the 8th floor.

*Announcement:*

You are invited to a:

** Distinguished Lecture Series by**

**Prof. David Jerison (MIT)**

**Abstracts**:

In Lecture 2 we will discuss how methods from geometric measure theory and elliptic regularity theory (developed for minimal surfaces) apply to level sets. We will focus on a version of the Harnack inequality that tells us how level surfaces influence each other. This gets us part way towards understanding hot spots.

**THE LECTURE WILL BE AT 16:30 AND NOT AT 15:30 AS INDICATED IN THE POSTER**

All lectures will be in Amado 232.

Light refreshments will be given in the faculty lounge on the 8th floor.

*Announcement:*

TBA...

*Announcement:*

You are invited to a:

** Distinguished Lecture Series by**

**Prof. David Jerison (MIT)**

**Abstracts**:

In Lecture 3 we will explain how complex analysis and differential geometry, in particularas developed for minimal surface theory, can be used to characterize global solutions andprove rigidity and regularity results for free boundaries. This gives further insights into themissing ingredients that will be needed to understand level sets of eigenfunctions.

All lectures will be in Amado 232.

Light refreshments will be given in the faculty lounge on the 8th floor.