Nov 20 2019

### Unique and 2:2 Games, Grassmannians, and Expansion

Speaker: Irit Dinur

2:00pm | Simonyi Hall 101
The unique games conjecture gives a very strong PCP theorem, which, if true, leads to a clean understanding of a broad family of approximation problems. We will describe recent progress on the conjecture and how certain type of expansion and hypercontractivity of the...

Nov 19 2019

### High Dimensional Expansion and Error Correcting Codes

Speaker: Irit Dinur

2:00pm | Simonyi Hall 101
High dimensional expansion generalizes edge and spectral expansion in graphs to higher dimensional hypergraphs or simplicial complexes. Unlike for graphs, it is exceptionally rare for a high dimensional complex to be both sparse and expanding. The only known such expanders...

Nov 18 2019

### The PCP theorem

Speaker: Irit Dinur

2:00pm | Simonyi Hall 101
The PCP theorem says that any mathematical proof can be written in a special "PCP" format such that it can be verified, with arbitrarily high probability, by sampling only a few symbols in the proof. Hence the name, Probabilistically Checkable Proofs (PCPs). Alternatively...

Oct 26 2018

### The Zilber-Pink conjecture

Speaker: Jonathan Pila

2:00pm | Simonyi Hall 101
The Zilber-Pink conjecture is a far reaching finiteness conjecture in diophantine geometry, unifying and extending Mordell-Lang and Andre-Oort. This lecture will state the conjecture, illustrate its varied faces, and indicate how the point-counting strategy can be applied to...

Oct 24 2018

### O-minimality and Ax-Schanuel properties

Speaker: Jonathan Pila

2:00pm | Simonyi Hall 101
This lecture will describe the historical context and some key properties of o-minimality. It will then describe certain results in functional transcendence, generalizing the classical results on exponentiation due to Ax, and sketch how they can be proved.

Oct 23 2018

### Point-counting and diophantine applications

Speaker: Jonathan Pila

2:00pm | Simonyi Hall 101
This introductory lecture will describe results about counting rational points on certain non-algebraic sets and sketch how they can be used to attack certain problems in diophantine geometry and functional transcendence.

Oct 18 2017

### On the mathematical theory of black holes III

Speaker: Sergiu Klainerman

2:00pm | S-101
I will discuss a recent result in collaboration with J. Szeftel concerning the nonlinear stability of the Schwarzschild spacetime under axially symmetric, polarized perturbations.The gravitational waves detected recently by LIGO were produced in the final faze of the inward...

Oct 17 2017

### On the mathematical theory of black holes II

Speaker: Sergiu Klainerman

2:00pm | S-101
I will discuss in some detail the main difficulties of the problem of nonlinear stability of black holes and the recent advances on the related issue of linear stability.The gravitational waves detected recently by LIGO were produced in the final faze of the inward spiraling...

Oct 16 2017

### On the mathematical theory of black holes I

Speaker: Sergiu Klainerman

2:00pm | S-101
On the reality of black holes. I will give a quick introduction to the initial value problem in GR and overview of the problems of Rigidity, Stability and Collapse and how they fit with regard to the Final State Conjecture.The gravitational waves detected recently by LIGO...

Mar 17 2016

### Weyl groups, and their generalizations, in enumerative geometry III

Speaker: Andrei Okounkov

4:00pm | S-101
These lectures will be about enumerative K-theory of curves (and more general 1-dimensional sheaves) in algebraic threefolds. In the first lecture, we will set up the enumerative problem and survey what we know and what we conjecture about it. In particular, we will meet the...