Time: 3:30 p.m. Place: Jeffery Hall 319
Speaker: Mike Roth (Queen's University)
Title: Zak’s theorems on tangencies IV
Abstract: We will finish the proof of Hartshorne’s conjecture on linear normality, and introduce the problem of computing the fundamental group of the complement of a nodal curve in the plane.
Time: 2:15 p.m. Place: Jeffery Hall 319
Speaker: François Séguin (Queen's University)
Title: Frequency of primes dividing n and $\Phi_n$.
Abstract: In a previous talk, we have seen that at most one prime Pn, can divide both an integer n and the nth cyclotomic polynomial evaluated at some integer a. During this talk, we will use methods in Dirichlet series to investigate how often Pn actually divides the nth cyclotomic polynomial $\Phi_n$.
Time: 3:30-5:00 p.m. Place: Jeffery Hall 319
Speaker: Mihai Popa (University of Texas, San Antonio)
Title: Permutations of Entries and Asymptotic Free Independence for Gaussian Random Matrices
Abstract: Since the 1980's, various classes of random matrices with independent entries were used to approximate free independent random variables. But asymptotic freeness of random matrices can occur without independence of entries: in 2012, in a joint work with James Mingo, we showed the (then) surprising result that unitarily invariant random matrices are asymptotically (second order) free from their transpose. And, in a more recent work, we showed that Wishart random matrices are asymptotically free from some of their partial transposes. The lecture will present a development concerning Gaussian random matrices. More precisely, it will describe a rather large class of permutations of entries that induces asymptotic freeness, suggesting that the results mentioned above are particular cases of a more general theory.
Time: 5:30 p.m. Place: Jeffery Hall 118
Speaker: Greg Smith (Queen's University)
Title: Realistic Expectations.
Abstract: How many real roots should we expect a real polynomial to have? In this talk, we will convert this vague question into a well-posed mathematical problem. With the help of geometry, we will also provide the surprisingly beautiful solution.
Time: 3:30 p.m. Place: Jeffery Hall 319
Speaker: Mike Roth (Queen's University)
Title: Zak's theorems on tangencies III
Abstract: We will prove Hartshorne’s conjecture on linear normality of subvarieties of small dimension, in the form of the restatement in terms of secant varieties.
Time: 2:15 p.m. Place: Jeffery Hall 319
Speaker: Arpita Kar (Queen's University)
Title: On the normal number of prime factors of Ramanujan Tau function.
Abstract: We will discuss various results concerning $\omega(\tau(p))$, $omega(\tau(n))$, $\omega(\tau(p+1))$ where $\tau$ denotes Ramanujan Tau function and $\omega(n)$ denotes the number of prime factors of $n$ counted without multiplicity. This is work in progress with Prof. Ram Murty.
Time: 3:30-5:00 p.m. Place: Jeffery Hall 319
Speaker: Jamie Mingo (Queen's University)
Title: The Infinitesimal Law of a real Wishart Matrix, II
Abstract: I will continue from last week and compute the infinitesimal cumulants.
Time: 2:15 p.m. Place: Jeffery Hall 319
Speaker: M. Ram Murty (Queen's University)
Title: The Central Limit Theorem in algebra and Number Theory.
Abstract: The central limit theorem is certainly one of the pinnacles of 20th century mathematics that has transformed human civilization extending its influence outside mathematics and now touching every other scientific discipline and beyond. I will give a short historical survey and then highlight how the central limit theorem has inspired the development of probabilistic number theory and probabilistic group theory. At the end, I will report on some old work with Kumar Murty and recent joint work with Arpita Kar and Neha Prabhu regarding arithmetical aspects of Fourier coefficients of modular forms.
Time: 3:30-5:00 p.m. Place: Jeffery Hall 319
Speaker: Jamie Mingo (Queen's University)
Title: The Infinitesimal Law of a real Wishart Matrix
Abstract: The Wishart ensemble is the random matrix ensemble used to estimate the covariance matrix of a random vector. Infinitesimal freeness is a generalized independence stronger than freeness but weaker than second order freeness. I will give the infinitesimal distribution of a real Wishart matrix. It is given in terms of planar diagrams which are 'half' of a non-crossing annular partition.
Time: 4:30 p.m. Place: Jeffery Hall 319
Speaker: Hugh Thomas (UQAM)
Title: The Robinson-Schensted-Knuth correspondence via quiver representations
Abstract: The Robinson--Schensted--Knuth correspondence is a many-faceted jewel of algebraic combinatorics. In one variation, it provides a bijection between permutations of $n$ and pairs of standard Young tableaux with the same shape, which is a partition of $n$. In another (more general) version, it provides a bijection between fillings of a partition $\lambda$ by arbitrary non-negative integers and fillings of the same shape $\lambda$ by non-negative integers which weakly increase along rows and down columns (i.e., reverse plane partitions of shape $\lambda$). I will discuss an interpretation of RSK in terms of the representation theory of type $A$ quivers (i.e., directed graphs obtained by orienting a path graph). This allows us to generalize RSK to other Dynkin types (plus a choice of minuscule weight), and is related to periodicity results for piecewise-linear toggling. I will not assume familiarity with either RSK or with quiver representations. This is joint work with Al Garver and Becky Patrias.
