Mathematics & Statistics Seminar Talks

Seminar: Working on What (WOW)
Lee K. Jones (UMass Lowell):On local statistical machine learning
Organizer: Emily Gunawan, email: emily_gunawan@uml.edu
September 18, 11 a.m. - Noon, Room: Southwick Hall 350W

Abstract: We first review some optimal finite sample accuracy bounds in Loader [1999] and J. [2009] for weighted k-nearest neighbor rules for estimating a function f at a fixed point x under “smoothness” assumptions and conditions of approximate linearity in the spherical neighborhood about x containing the k nearest neighbors. Such bounds are ancillary i.e.depend only on the design points and not on the responses (unlike many obtained in logistic regression and with variance/bias tradeoff plug-in estimates). We extend these results here to include neighborhoods which consist of the convex hull of x and any sub-collection of the neighbors. These new bounds can be computed using Karmarkar’s linear programming algorithm (with a quadratic constraint ) and minimization of a non-smooth convex function. The convex minimization problem, using optimization algorithms of Nesterov (2004), is slower than that for smooth convex functions but is achievable with today’s computers. We conjecture that an appropriate greedy relaxed approach converges at a faster rate. We can show that speed-ups using proximal functions ( as are used in global machine learning e.g. lasso regression, inverse problems, matrix completions, etc.) are not possible.

We indicate how to implement both the old and new results for binary classification problems or proportions sampling and search over lower dimensional subspaces of the design domain for accurate estimates of conditional success probability given the projection of x.

Seminar: Working on What (WOW)
Jim Propp (UMass Lowell):“Tilings? (Again?)”
Organizer: Emily Gunawan, email: emily_gunawan@uml.edu
October 23, 11 a.m. - Noon, Room: Southwick Hall 350W

Abstract: From the late 1980s to the early 2000s I did a lot of work on tiling. For the next 20 years I did very little work in this area. Suddenly I’m working on tilings again. What’s up with that?

Seminar on Algebraic Combinatorics
Benjamin Dequêne (University of Picardie Jules Verne): A generalized RSK correspondence via the combinatorics of (type A) quiver representations
Organizer: Emily Gunawan, email: emily_gunawan@uml.edu
January 24, 11 a.m. - Noon, Room: Southwick Hall 350W

Abstract: The Robinson-Schensted-Knuth (RSK) correspondence is a bijection from nonnegative integer matrices to pairs of semi-standard Young tableau. A generalized version of RSK gives a bijection from fillings of a tableau of shape lambda to reverse plane partitions of shape lambda.

From the quiver representation point of view, the RSK correspondence provides a transformation between two different invariants of a module X (in a certain subcategory). The entries in the arbitrary filling of shape lambda correspond to multiplicities of indecomposable summands of the representation, while the entries in the reverse plane partition of shape lambda record the generic Jordan form data of X, an invariant introduced by Garver, Patrias and Thomas.

My talk aims to present a version of RSK that works from the most general possible choice of a subcategory of the category of representations of a type A quiver. Note that this talk will not assume that the audience has prior knowledge of quiver representations.

This is a combinatorial extraction (in progress) of my Ph.D. work, supervised by Hugh Thomas.

Seminar: Working on What (WOW)
Daniel Glasscock (UMass Lowell): Difference sets: not Bohring but potentially Bohr
Organizer: Emily Gunawan, email: emily_gunawan@uml.edu
February 21, 11 a.m. - Noon, Room: Southwick Hall 350W

Abstract: It is a basic and often useful fact in analysis that convolutions make things smoother. Less famous is the additive combinatorial analogue: set sums and differences support richer structures (and, hence, are “smoother”). This fact – known almost a century ago – is still being refined and finding new applications in additive number theory today. And there are still many open questions. In this talk, we will discuss the following open question: must the difference set A-A of a syndetic subset of integers A contain a Bohr set?

Seminar: Working on What (WOW)
Amanda Redlich (UMass Lowell): Eeny-Meeny-Miney-Moe: Random approaches to solving hard problems
Organizer: Emily Gunawan, email: emily_gunawan@uml.edu
March 20, 11 a.m. - Noon, Room: Southwick Hall 350W

Abstract: Some problems seem impossibly hard: computing the Ramsey number R(5,5), modeling the internet, picking a grocery store checkout line. It turns out that using random guesses is a great approach to all three of these! A lot of my research uses randomized algorithms and the probabilistic method. In this talk I'll give an overview of some of the classical results in the area.

Seminar on Analysis and Applications
Yuan Liu (Wichita State University): High order structure-preserving numerical methods for convection-diffusion-reaction equations
Organizer: Shiwen Zhang, email: shiwen_zhang@uml.edu
April 1, 11 a.m. - Noon, Room: Southwick Hall 350W

Abstract: Convection-diffusion-reaction (CDR) equation is one of the widely used mathematical models in science and engineering. It describes how one or more substances distributed under the influences of convection, diffusion and reaction processes. In this talk, we will present some recent work on high order numerical methods for solving CDR equation under two cases. (1) When there are only convection terms, the CDR equation is hyperbolic conservation laws. We will talk about the development of high order bound-preserving numerical methods. (2) When there are only diffusion and reaction terms, Krylov implicit integration factor discontinuous Galerkin methods on sparse grids are proposed to solve the equation in high dimensional cases.

Seminar: Working on What (WOW)
Tibor Beke (UMass Lowell): Hex
Organizer: Emily Gunawan, email: emily_gunawan@uml.edu
April 24, 11 a.m. - Noon, Room: Southwick Hall 350W

• a thoroughly enjoyable board game
• a case study in taking the continuum limit of a discrete theorem (the fact that no Hex game can end in a draw is "equivalent" to the Brouwer Fixed Point theorem)
• a case study in game theory (the so-called "strategy stealing" argument proves that the first player has a winning strategy)
• a case study in computational complexity (finding the winning move is PSPACE-complete, probably explaining why no explicit winning strategy has been found beyond 10x10 boards).