Past Events

In this talk, we will discuss an estimate for a discrete mean value of the Riemann zeta function and its derivatives multiplied by Dirichlet polynomials. Assuming the Riemann Hypothesis, we obtain a lower bound for the 2kth moment of all the...

In the previous talk, we got comfortable with the category of Artin local rings. In this second part, we will move on to functors of Artin rings, deformation functors, and some examples. Time permitting, we will discuss Schlessinger's theorem, giving...

Every group admits a unitary representation on a Hilbert space. In other words, every group can be realized concretely as symmetries on a Hilbert space. From these representations we can construct objects known as C*-algebras. This invites the use of...

The word complexity function p(n) of a subshift X measures the number of n-letter words appearing in sequences in X, and X is said to have linear complexity if p(n)/n is bounded. It's been known since work of Ferenczi that linear word complexity...

We say that a knot is slice if it bounds a smooth disk in 4-ball and ribbon if it bounds a ribbon disk in 3-sphere. Ribbon knots are always slice, while it is unknown whether the converse, also known as the slice-ribbon conjecture, is true. The...

Cell locomotion is essential for early development, angiogenesis, tissue regeneration, the immune response, and wound healing in multicellular organisms, and plays a very deleterious role in cancer metastasis in humans. Locomotion involves the...

We will explore how a Fourier optimization framework may be used to study two classical problems in number theory involving Dirichlet characters: The problem of estimating the least character non-residue; and the problem of estimating the least prime...

The memory capacity of a statistical model is the largest size of generic data that the model can memorize and has important implications for both training and generalization. In this talk, we will prove a tight memory capacity result for two-layer...

A polytope is the convex hull of finitely many points. A polytope is simplicial if all of its faces are simplices. What partial information about a simplicial polytope P is enough to uniquely determine P (up to certain equivalences)? We will discuss...

The formalization of string diagrams, in a 1991 paper by Andre Joyal and Ross Street, was a seminal event. They defined a basic diagrammatic language and proved its validity for rigorous mathematics in any monoidal category, and in doing so they laid...