Seminars Sorted by Series

A matrix M is rigid if one needs to change it in many places in order to reduce its rank significantly. While a random matrix M (say over a finite field) is rigid with high probability, coming up with explicit constructions of such matrices is still...

Cubic forms are homogeneous polynomials of degree 3 in several 
variables. Number theory is interested in their zeros over the rational 
numbers. Algebraic geometry studies the cubic hypersurfaces defined by 
them (e.g., the 27 lines on smooth cubic...

We discuss a modern perspective on the winding number on $S^1$ for maps that may not be continuous. This reveals a surprising connection to Fourier analysis and motivates the question: is the winding number determined by the moduli of the Fourier...

Consider a right angled cylinder. Glue the ends together after twisting many times to form a flat torus $C^1$-isometrically embedded in $R^3$. What can we say about the global geometry of this embedding?

There is a remarkable parallel, first explicitly enunciated in the 1960s, between algebraic number theory and 3-dimensional geometry; for example, prime numbers are considered analogous to knots. I will only say a few short words about the substance...

Some people think that the brain is something like a (conscious) computer. But if a brain can compute, why can't a rock, or a river stream? This basic question has been considered by philosophers, physicists, and mathematicians.

It is not entirely...

The Alexandrov-Fenchel inequality---the fundamental log-concavity phenomenon in convex geometry---arose from Minkowski's work in number theory in the late 1800s. It has resurfaced in surprising ways throughout the 20th and 21st centuries in the...

You are swimming at the center of a circular lake with a bear waiting on the shore. The bear, unable to swim, moves four times faster on land than you do in water, but once on land, you can outrun it. Can you escape?

This classic riddle has been...

The Ricci curvature of a Riemannian manifold is best viewed as the right replacement for the (nonlinear) laplacian of the metric g, which in particular explains why it so often appears in geometry and analysis.  Most commonly one studies either...

How much information is needed to describe a trajectory in a dynamical system? The answer depends on what one means by dynamical system.

If our system is a probability measure space, and one has a time evolution (with either discrete or continuous...

In primary school, I never got beyond adding integers and the questions have only been piling up since! What do sets of integers $A$ look like if they generate only a few sums with the elements of another set $B$? Meester Jaap (my primary teacher)...

The polar body is a fundamental concept in functional and convex analysis, representing a special convex set associated with any convex subset of Euclidean space. One can think of the polar operation as, roughly speaking, the "inverse" of convex...

I will explore two questions about projections of geometric objects in 4-dimensional spaces:

(1) Let $A$ be a convex body in $\mathbb{R}^4$, and let $(p_{12}, p_{13}, p_{14}, p_{23}, p_{24}, p_{34})$ be the areas of the six coordinate projections of...

In the 1960's, Quillen found a remarkable relationship between a certain class of cohomology theories and the theory of formal groups. This discovery has had a profound impact on algebraic topology. In this talk, I'll give a brief exposition of...

After a short crash course in using Lean to formalize mathematics, we will discuss potential applications to and implications for mathematics education, publication, and research.

What are some of the ways in which binary-valued functions can accurately approximate continuous-valued ones? This talk will be a gentle exposition of the mathematics of "noise-shaping quantization" presented through motivating applications. We will...

Sand drawings appear in many cultures coming, for instance, from South India, Oceania, and Africa.

We will focus on the Chowke people who have a beautiful tradition that combines mathematics and storytelling. In their free time, they would engage in...

Stable commutator length (or scl) of group elements is a well-known, simple-to-define invariant, related to bounded cohomology and quasimorphisms. Yet its simple definition is a trap: many of the exciting developments around scl required "better"...

The theory of quantum cohomology was developed in the early 1990s by physicists working in the field of superstring theory.

Mathematicians then discovered applications to enumerative geometry, counting the number of rational curves of a given degree...

Expansion is an important notion in graphs, and comes in several equivalent formulations, including (1) convergence of random walks, (2) having no small cuts, and (3) having a large spectral gap. I will talk about a higher dimensional generalization...

We will consider finite collections of squares tiles, and ask when we can tile the whole plane in an interesting way. This question is related to the algebraic structure of ‘lattices in products of trees’, which are discrete groups acting...

Gaussian periods are certain sums of roots of unity.  Gauss introduced them in his work on straight edge and compass constructions of regular polygons.  Since then, Gaussian periods have played important roles in number theory and beyond.  It turns...

An open book is a topological concept aptly named by Elmar Winkelnkemper.

The binding of the book is a fibred knot (of any dimension), and open books and fibred knots are essentially synonymous. Currently the standard reference for the existence and...

There is a deep connection between stable homotopy theory and the theory of formal groups, first noticed by Quillen. I will describe this connection, and explain how this has led to the chromatic picture of the stable homotopy category.

In this talk, I’ll describe one of the most surprising algorithms in computer science: a way to count arbitrarily high while maintaining just three bits of state and a clock. It turns out that the main idea behind the algorithm also appears in a...

I will talk very briefly about what number theorists call special values of $zeta$ and L-functions. I will start with some familiar, classical equalities and will attempt to touch upon some less familiar (mostly conjectural and very far reaching)...

Alexander Grothendieck was one of the greatest thinkers, and one of the most unusual personalities, in the history of science.  In addition to some biographical details, this talk will offer a perspective on his approach to mathematics.

I will start with an interesting symmetry of plane quadrilaterals and see what mathematics we can reach within 20 minutes.   Also I will explain the title.