Video Lectures

Cohomology for computer science

November 17, 2015

Alex Lubotzky

We will start with presenting the basic notions of (co)homomology of simplical complexes (which requires only basic linear algebra over the field of order 2) and then we will indicate its relevance for several topics in computer science and...

video lecture

The $\mathrm{SL}(2,\mathbb R)$ action on moduli space

November 16, 2015

Alex Eskin

There is a natural action of the group $\mathrm{SL}(2,\mathbb R)$ of $2 \times 2$ matrices on the unit tangent bundle of the moduli space of compact Riemann surfaces. This action can be visualized using flat geometry models, which allows one to make...

video lecture

How quaternion algebras over number fields are useful for creating compiler for a quantum computer?

November 16, 2015

Vadym Kliuchnikov

Solving the following problem is crucial when compiling for a quantum computer: given a finite set $G$ of elements of $SU(2)$, target element $U$ from $SU(2)$ and real number $\epsilon$ find $g_1,\dotsc, g_N$ from $G$ such that $\| g_1 \dotsm g_N -...

video lecture

THE ART OF DINING: Downton Abbey

November 13, 2015

Francine Segan

Join returning speaker Francine Segan and discover the elaborate etiquette, enchanting entertainments, and dishes Mrs. Patmore would have been proud to send to the table. Vivid descriptions of Lord Grantham-esque dinner parties, cotillions, and...

video lecture

Algebraic degrees and Galois conjugates of pseudo-Anosov stretch factors

November 12, 2015

Balazs Strenner

We consider questions that arise naturally from the subject of the first talk. The have two main results: 1. In genus $g$, the algebraic degrees of pseudo-Anosov stretch factors include all even numbers between $2$ and $6g - 6$; 2. The Galois...

video lecture

Pseudo-Anosov constructions and Penner's conjecture

November 12, 2015

Balazs Strenner

In this first talk, we give an introduction to Penner’s construction of pseudo-Anosov mapping classes. Penner conjectured that all pseudo-Anosov maps arise from this construction up to finite power. We give an elementary proof (joint with Hyunshik...

video lecture

Hard Lefschetz theorem and Hodge-Riemann relations for combinatorial geometries

November 09, 2015

June Huh

A conjecture of Read predicts that the coefficients of the chromatic polynomial of a graph form a log-concave sequence for any graph. A related conjecture of Welsh predicts that the number of linearly independent subsets of varying sizes form a log...

video lecture

Cutting plane method: A faster algorithm for many (combinatorial) optimization problems

November 09, 2015

Yin Tat Lee

Many polynomial-time solvable (combinatorial) optimization problems can be reduced to the feasibility problem and the intersection problem. In this talk, I will present the first nearly cubic time algorithm for both problems using a new cutting...

video lecture

Topological and combinatorial methods in Theoretical Distributed Computing

November 07, 2015

Dmitry Feichtner-Kozlov

In the first half of the talk I will give a very compressed introduction into parts of Theoretical Distributed Computing from the point of view of mathematician. I will describe how to construct simplicial models whose combinatorics contains...

video lecture

Critical mechanical structures: topology and entropy

November 07, 2015

Xiaoming Mao

Critical mechanical structures are structures at the verge of mechanical instability. These structures are characterized by their floppy modes, which are deformations costing little energy. On the one hand, numerous interesting phenomena in soft...