Previous Conferences & Workshops

Oct
26
2022

Workshop on Additive Combinatorics and Algebraic Connections

On Tensor Properties Preserved Under Linear Maps
2:00pm|Simonyi 101 and Remote Access

Abstract: A theorem by Kazhdan and Ziegler says that any property of homogeneous polynomials---of a fixed degree but in an arbitrary number of variables---that is preserved under linear maps is either satisfied by all polynomials or else implies a...

Oct
26
2022

Probability Seminar

3-Webs and the Boundary Measurement Matrix
Richard Kenyon
11:15am|West Lecture Hall

This is joint work with Haolin Shi (Yale). 3-webs are bipartite, trivalent, planar graphs. They were defined and studied by Kuperberg who showed that they correspond to invariant functions in tensor products of $SL_3$-representations. Webs and...

Oct
26
2022

Workshop on Additive Combinatorics and Algebraic Connections

G-stable Rank and the Cap Set Problem
Harm Derksen
11:15am|Simonyi 101 and Remote Access

Abstract: Ellenberg and Gijswijt drastically improved the best known upper asymptotic bound for the cardinality of a cap set in 2016. Tao introduced the notion of slice rank for tensors and showed that the Ellenberg-Gijswijt proof can be nicely...

Oct
26
2022

Workshop on Additive Combinatorics and Algebraic Connections

Tensorial Forms in Infinite Dimensions
Andrew Snowden
10:00am|Simonyi 101 and Remote Access

Abstract: Let V be a complex vector space and consider symmetric d-linear forms on V, i.e., linear maps $Sym^d(V) \rightarrow > C$. When V is finite dimensional and $d>2$, the structure of such forms is very complicated. Somewhat surprisingly, when...

Oct
25
2022

Workshop on Additive Combinatorics and Algebraic Connections

The Alon-Jaeger-Tarsi Conjecture via Group Ring Identities
Peter Pach
4:00pm|Simonyi 101 and Remote Access

Abstract: The Alon-Jaeger-Tarsi conjecture states that for any finite field $F$ of size at least 4  and any nonsingular  matrix $M$ over $F$ there exists a vector $x$ such that neither $x$ nor $Mx$ has a 0 component. In this talk we discuss the...

Oct
25
2022

Workshop on Additive Combinatorics and Algebraic Connections

The Monomial Structure of Boolean Functions
2:00pm|Simonyi 101 and Remote Access

Abstract: Let $f:{0,1}^n$ to ${0,1}$ be a boolean function. It can be uniquely represented as a multilinear polynomial. What is the structure of its monomials? This question turns out to be connected to some well-studied problems, such as the log...

Oct
25
2022

Workshop on Additive Combinatorics and Algebraic Connections

Ranks of Tensors
11:15am|Simonyi 101 and Remote Access

Abstract: Several equivalent definitions of rank for matrices yield non-equivalent definitions of rank when generalized to higher order tensors. Understanding the interplay between these different definitions is related to important questions in...

Oct
25
2022

Workshop on Additive Combinatorics and Algebraic Connections

Polynomial Maps With Noisy Input-Distributions
Jop Briet
10:00am|Simonyi 101 and Remote Access

Abstract: A problem from theoretical computer science posed by Buhrman asks to show that a certain class of circuits (NC0[+]) is bad at decoding error correcting codes under random noise. (This would be in contrast with an analogous class of quantum...

Oct
24
2022

Joint IAS/Princeton University Symplectic Geometry Seminar

Symplectic Embeddings and Toric Resolutions
Marco Castronovo
4:00pm|Fine 314 and Remote Access

I will first review the recent construction of polyhedral Liouville domains, which are subdomains of a complex torus whose boundary dynamics encodes the singularities of a toric compactification. I will then report on work in progress aimed at...

Oct
24
2022

Workshop on Additive Combinatorics and Algebraic Connections

The Failure of the Periodic Tiling Conjecture
2:00pm|Simonyi 101 and Remote Access

Abstract: Translational tiling is a covering of a space using translated copies of a building block, called a "tile", without any positive measure overlaps. What are the possible ways that a space can be tiled?
The most well known conjecture in this...