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.