Infosheet (January 30th, 2018) |
Queen's University - Department of Mathematics and Statistics |
Tuesday, January 30 |
Seminar in Free Probability and Random Matrices Time: 3:30 p.m. Place: Jeffery 319 |
Speaker: Neha Prabhu, Queen’s University Title: Semicircle distribution in number theory, Part II Abstract Attached |
Wednesday, January 31 |
Number Theory Seminar Time: 2:15 p.m. Place: Jeffery 319 |
Speaker: Vaidehee Thatte Title: Defect Extensions - I Abstract Attached |
Thursday, February 1 |
Math Club Time: 5:30 p.m. Place: Jeffery 118 |
Speaker: Peter Taylor Title: The sum of the cubes is the square of the sum Abstract Attached |
Friday, February 2 |
Dynamics Seminar Time: 10:30 a.m. Place: Jeffery 422 |
Speaker: Francesco Cellarosi Title: Limit theorems for rotations Abstract Attached |
Friday, February 2 |
Department Colloquium Time: 2:30 p.m. Place: Jeffery 234 |
Speaker: Jory Griffin, Queen’s University Title: The Lorentz Gas – Macroscopic Transport from Microscopic Dynamics Abstract Attached |
Monday, February 5 |
Geometry and Representation Theory Seminar Time: 4:30 p.m. Place: Jeffery 319 |
Speaker: David Wehlau Title: Khovanski Bases and Derivations Abstract Attached |
Wednesday, February 7 |
Curves Seminar Time: 3:30 p.m. Place: Jeffery 319 |
Speaker: Daniel Erman, Wisconsin – Madison Title: Big polynomial rings and Stillman’s conjecture Abstract Attached |
Items for the Info Sheet should reach Anne ( burnsa@queensu.ca) by noon on Monday. The Info Sheet is published every Tuesday.
Tuesday, January 30, 3:30 p.m. Jeffery 319
Seminar in Free Probability and Random Matrices
Speaker: Neha Prabhu
Title: Semicircle distribution in number theory, Part II
Abstract: In free probability theory, the role of the semicircle distribution is analogous to that of the normal distribution in classical probability theory. However, the semicircle distribution also shows up in
number theory: it governs the distribution of eigenvalues of Hecke operators acting on spaces of modular cusp forms. In this talk, I will give a brief introduction to this theory of Hecke operators and sketch the proof of a result which is a central limit type theorem from classical probability theory, that involves the semicircle measure.
Wednesday, January 31, 2:15 p.m. Jeffery 319 - Number Theory Seminar
Speaker: Vaidehee Thatte
Title: Defect Extensions – I
Abstract: Let $K$ be a valued field of characteristic $p > 0$ with henselian valuation ring $A$. Let $L$ be a non-trivial Artin-Schreier extension of $K$ with $B$ as the integral closure of $A$ in $L$. In
the classical theory of complete discrete valuation rings, $B$ is generated as an $A$-algebra by a single element. This in particular, is not true in the defect case. We will discuss a result that allows us to write $B$ as a "filtered union over $A$", when there is defect.
Similar results can be obtained in the mixed characteristic case.
Thursday, February 1, 5:30 p.m. Jeffery 118 - Math Club
Speaker: Peter Taylor
Title: The sum of the cubes is the square of the sum
Abstract: We have all seen the lovely formula: 13+23+33+⋯+n3=(1+2+3+⋯+n)2. Often attributed to the Greek mathematician Nicomachus of Gerasa (circa AD 100). Is this a "one-off" result or are there other simple examples of a sequence for which the sum of the cubes is the square of the sum? We will see that there are some unexpectedly simple examples of such sequences.
Friday, February 2, 10:30 a.m. Jeffery 422 - Dynamics Seminar
Speaker: Francesco Cellarosi
Title: Limit theorems for rotations
Abstract: I will review the rich literature on the various limit theorems one can achieve for ergodic averages of irrational rotation of the circle.
Friday, February 2, 2:30 p.m. Jeffery 234 - Department Colloquium
Speaker: Jory Griffin
Title: The Lorentz Gas – Macroscopic Transport from Microscopic Dynamics
Abstract: The Lorentz Gas is microscopic model for conductivity in which a point particle representing an electron moves through an infinite array of scatterers representing the background medium. On the macroscopic scale the dynamics can instead be modelled by the linear Boltzmann transport equation, an irreversible equation where motion of particles appears to be stochastic. How can these two pictures be reconciled? Can we 'derive' the macroscopic picture from the microscopic one? I will talk about the solution to this problem as well as its quantum mechanical analogue where much less is currently known.
Monday, February 5, 4:30 p.m. Jeffery 319 - Geometry and Representation Theory Seminar
Speaker: David Wehlau
Title: Khovanski Bases and Derivations
Abstract: Let $R=K[x_1,,\dots,x_m,y_1,\dots,y_m,z_1,\dots,z_m]$ be a polynomial algebera over a field $K$ of characteristic zero, Let $\Delta$ be the locally nilpotent derivation on $R$ determined by $\Delta(z_i) = y_i$, $\Delta(y_i) = x_i$ and $\Delta(x_i)=0$ for $i=1,2,\dots,m$. This is an example of
a Weitzenb\"ock derivation. We exhibit a minimal set of generators $\mathcal G$ for the algebra of
constants $R^\Delta = \ker \Delta$. We also construct a Khovanski (or sagbi) basis for this algebra.
Even though this basis is infinite our proof yields an algorithm to express
any element of $R^\Delta$ as
a polynomial in the elements of $\mathcal G$. In particular, this method
shows how the classical techniques of polarization and restitution may be
used in combination with Khovanski bases to yield a constructive method for
expressing elements of a subalgebra as a polynomials in its generators.
Wednesday, February 7, 3:30 p.m. Jeffery 319 - Curves Seminar
Speaker: Daniel Erman
Title: Big polynomial rings and Stillman’s conjecture
Abstract: Ananyan–Hochster's recent proof of Stillman's conjecture is based on a key principle: if f_1,.., f_r are sufficiently general forms in a polynomial ring, then as the number of variables tends to infinity, they will behave increasingly like independent variables. We show that this principle becomes a theorem if ones passes to a limit of polynomial rings, using either the inverse limit or the ultraproduct. This yields the surprising fact that these limiting rings are themselves polynomial rings (in uncountably many variables). It also yields two new proofs of Stillman's conjecture. This is joint work with Steven Sam and Andrew Snowden.