Special Topics Courses

Fall 2019

MA 591-001: Math Analysis II, Bevin Maultsby, MWF 11:45-12:35

Calculus of several variables, topology in n-dimensions, limits, continuity, differentiability, implicit functions, integration. Cross-listed with MA 426.

MA 591-002: Fixed income products & analysis, R. Ellson, MW: 8:30-9:45

MA 591-003: Topological combinatorics, P. Hersh, MW 1:30-2:45

This class will focus on a rich interplay between topology and combinatorics. This will include combinatorial techniques including shellability, discrete Morse theory, and the Quillen Fiber Lemma, among others for computing homotopy type, homology groups and Betti numbers of simplicial complexes and cell complexes. Going in the other direction, we explore how the Mobius function of a partially ordered set is interpreted topologically. We will spend considerable time on hyperplane arrangements and geometric lattices first (from both an enumerative and a topological viewpoint), and then on poset topology more generally later in the semester. Along the way, we will do a quick review of representation theory of the symmetric group, to the extent it will be needed in our study of poset topology. For students who have taken topology and would like to understand things in a very concrete, hands-on way with lots of examples, this course could be useful. It would be helpful (but not absolutely necessary) to have previously taken MA 753; it is not necessary to have previously taken MA 524/724.

MA 591-004: Scientific programming with Python, A. Saibaba, F: 1:55-2:45

MA 792-001: Algebraic topology II, T. Lidman, MW: 11:45-1:00

In this course, we will develop powerful tools for studying algebraic and topological problems by building deep connections between the two areas. Beginning with a development of cohomology and higher homotopy groups, we will be able to characterize when two spaces are homotopy equivalent and also bound the minimal number of relations needed to present a group. From here we will develop more advanced algebraic and topological tools which have applications to topology, geometry, combinatorics, algebraic geometry, representation theory, and more. Potential topics include: cohomology, homotopy theory, group cohomology, vector bundles, characteristic classes, spectral sequences, spectra, K-theory, topology of manifolds. The content will be somewhat guided by the interests of the constituents. Prerequisites: MA 753.

MA 793-001: Viscosity solutions, T. Nguyen, MF: 3:00-4:15

MA 797-001: Convex optimization methods in data science, P. Combettes, TTh: 10:15-11:30

MA 810-001: Foundations of deep learning, M. Haider, M: 4:30-7:15

This course will be offered at SAMSI. It will start with a review of standard neural networks, and then progress to modern deep learning, including convolutional neural networks, recursive neural networks, generative adversarial networks, and various kinds of autoencoders. We shall discuss training strategies, architecture search, regularization and quantization.