Geometry and Combinatorics

Speaker: Ahmed Umer Ashraf (Western)

"CSM classes for matroids"

Time: 15:30

Room: MC 108

TBA

Quantum Geometry

Speaker: Masoud Khalkhali (Western)

"Combinatorics of Feynman diagrams and quantum field theory VI"

Time: 11:00

Room: MC 108

Geometry and Topology

Speaker: Avi Steiner (Western)

"Intersection cohomology, characteristic cycles, and affine cones"

Time: 15:30

Room: MC 107

Intersection cohomology, invented by Goresky and MacPherson, is a notion of cohomology for singular spaces which admits generalizations of classical theorems such as Poincare duality and the Lefschetz hyperplane theorem. It is constructed by taking global sections of a certain perverse sheaf called the intersection cohomology complex. This complex is itself an interesting topological invariant, and to study it one often looks at its characteristic cycle. In particular, if X is the affine cone over a projective variety Y, one can look at the multiplicity of this cycle over the vertex of X. I will discuss a conjecture of mine which would describe how this multiplicity changes with the projective embedding of Y, along with some evidence for the conjecture being true coming from the normal toric case.

Algebraic Geometry

Speaker: Nicole Lemire (Western)

"Adam's operations and the Gamma Filtration"

Time: 15:30

Room: WSC 187

Geometry and Combinatorics

Speaker: (Western)

"No talk this week (reading week)"

Time: 15:30

Room: MC 108

Quantum Geometry

Speaker: Masoud Khalkhali (Western)

"Matrix Integrals and Random Matrix Theory"

Time: 11:00

Room: MC 108

Geometry and Combinatorics

Speaker: Ahmed Umer Ashraf (Western)

"CSM classes of matroids II"

Time: 15:30

Room: MC 108

Last time we defined what it means to be a Minkowski weight over a k-skeleton of a fan (complete or not). To a loopless matroid, there is an associated simplicial fan called Bergman fan. Following de Medrano, Rincon and Shaw we will define the CSM classes of a loopless matroid as Minkowski weights over this fan. We will show that it satisfies the balancing condition. This will involve some combinatorial machinery concerning matroid that we will review.

Quantum Geometry

Speaker: Masoud Khalkhali (Western)

"Matrix Integrals and Random Matrix Theory II"

Time: 11:00

Room: MC 108

Geometry and Topology

Speaker: Luis Scoccola (Western)

"Stability of topological invariants of data"

Time: 15:30

Room: MC 107

Topological Data Analysis provides a framework for analyzing data that is robust to perturbations of the data. One way in which it accomplishes this is by introducing stable invariants: invariants of data sets that vary continuously with respect to suitable metrics on the collection of data sets. In this talk I will present several well known invariants of different kinds of data (such as metric spaces, metric measure spaces, dynamic metric spaces, and filtered metric spaces) and a theoretical framework that lets us prove known stability results as well as novel ones.

Colloquium

Speaker: Sylvie Paycha (Potsdam)

"Exploring the geometry of regularity structures"

Time: 15:30

Room: MC 108

Regularity structures were introduced by Martin Hairer to deal with the divergences that arise from stochastic partial differential equations which typically involve white noise. Exploring the underlying geometry reveals the role played in this context by direct connections on a vector bundle. Originally introduced by Nikolai Teleman in the context of non commutative geometry, these provide a direct transport of fibres from point to point. We generalise them to groupoids and propose an interpretation of re-expansion maps arising in regularity structures in the language of groupoids. Re-expansion maps were introduced by Hairer to transform a singular stochastic differential equation into a fixed point problem, based on an ad hoc ``Taylor expansion'' of the solutions at any point in space-time and a ``re-expansion map'' which relates the values at different points. For gauge groupoids, namely those built from a principal bundle, a re-expansion map can be viewed as a (local) ``gaugeoid field'', the groupoid counterpart of a (local) gauge field. We investigate the case of jet bundles arising in polynomial regularity structures.

Geometry and Combinatorics

Speaker: Ahmed Umer Ashraf (Western)

"CSM classes for matroids III"

Time: 15:30

Room: MC 108

a continuation of last week's talk

Quantum Geometry

Speaker: Masoud Khalkhali (Western)

"Matrix Integrals and Random Matrix Theory III"

Time: 11:00

Room: MC 108

Geometry and Topology

Speaker: Daniel Fuentes-Keuthan (Johns Hopkins University)

"Understanding Goodwillie Towers of Infinity Categories"

Time: 15:30

Room: MC 107

In a foundational series of papers Goodwillie laid the grounds for a theory of "Taylor Series" for homotopy theory, defining a tower of functors which interpolate between the stable and unstable homotopy type of a functor. Work of Heuts refined this picture by associating to an infinity category a tower of infinity categories which interpolate between the stabilization and the category in a compatible way. Key to the understanding of this tower is a sequence of natural transformations referred to as "Tate diagonals". I will describe some attempts to understand these Tate diagonals, and if time permits some relations between Heuts tower and the homotopy nilpotent groups of Biederman and Dwyer.

Algebraic Geometry

Speaker: Nicole Lemire (Western)

"Adam's operations and the Gamma Filtration"

Time: 15:30

Room: WSC 187

Geometry and Combinatorics

Speaker: Ahmed Umer Ashraf (Western)

"CSM classes for matroids IV"

Time: 15:30

Room: MC 108

A new proof of the theorem of Lopez de Medrano, Rincon and Shaw.

Quantum Geometry

Speaker: Masoud Khalkhali (Western)

"Matrix Integrals and Random Matrix Theory IV"

Time: 11:00

Room: MC 108

Pizza Seminar

Speaker: Masoud Khalkhali (Western)

"Lattices, sums of square, shapes of drums, and theta functions"

Time: 16:30

Room: MC 204

The above list of connections is only a few of the fascinating links that connect the magnificent theta functions to questions in various areas of mathematics and physics. In this talk we shall explore some of these links, starting with the definition of basic theta functions and their properties. This talk should be accessible to all our undergraduate students.

Geometry and Topology

Speaker: Matthias Franz (Western)

"The cohomology rings of smooth toric varieties"

Time: 15:30

Room: MC 107

Toric varieties are complex varieties with a torus action that are defined by convex-geometric objects called fans. Twenty years ago, Buchstaber and Panov proposed a formula for the cohomology ring of a smooth toric variety in terms of a torsion product involving the Stanley-Reisner ring given by the fan. We show that their formula gives the correct cup product if 2 is invertible in the chosen coefficient ring, but not in general. We rectify this by defining an explicit deformation of the canonical multiplication on the torsion product. Along the way, we will give important advice to grad students.

Colloquium

Speaker: David Bellhouse (Western)

"Abraham De Moivre's Normal Approximation to the Binomial"

Time: 15:30

Room: MC 108

In 1718 Abraham De Moivre published his Doctrine of Chances, a work on probability theory. Many of the problems solved in the book had been given to him as challenge problems by mathematically inclined friends and patrons. After the book was published, challenge problems continued to flow in. One such problem was given to him by Sir Alexander Cuming in 1721: Two players of equal skill play 𝑛 games. At the end of these games, the player who wins the majority of these games gives a spectator a number of units of money corresponding to the difference between the number of games the player has won and 𝑛/2. What is the expected amount of money the player is to receive? Cuming also generalized the question to players of unequal skill. De Moivre’s solution to the original and generalized problem, for large 𝑛, is the normal approximation to the binomial, which he obtained in 1733. In this talk, I will give the historical background to the normal approximation to the binomial and De Moivre’s method of solution, as well as Thomas Bayes’s criticism of the result.