Special Offerings

2026-2027 Special Course Offerings 

(Subject to change, check the time schedule for most current information.)

Undergraduate Special Topics

 

Spring 2027, Math 480A: Computational Algebraic Geometry

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Polynomial equations and their solutions are fundamental objects in mathematics and appear across a wide range of applications. As in linear algebra, solutions to equations can be understood geometrically using tools from algebra. The solution sets of nonlinear equations in multiple variables have more interesting geometry and require us to develop new tools. In this class, we will learn how to understand and work with polynomial systems of equations using a mix of algebra, geometry, and algorithms and explore some real-world applications, such as to robotics and computer vision. This class is open to everyone who knows linear algebra and is familiar with mathematical proofs.

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Prerequisite: a minimum grade of 2.0 in either MATH 334, or both MATH 208 and MATH 300. 

 

 

Spring 2027, Math 336/480C: Functional Analysis 

Functional analysis provides tools for studying linear and nonlinear problems on infinite-dimensional (normed) vector spaces. This framework underlies much of modern analysis, differential equations, and quantum mechanics. Topics covered include: normed spaces, completeness, linear functionals, Hahn-Banach Theorem, duality, operators; Hilbert spaces; compact and self-adjoint operators; and the Spectral Theorem. If time allows, additional topics may include Lebesgue integration and/or applications to Fourier theory. 

Prerequisites: minimum grade of 2.0 in MATH 335 or MATH 425 

Spring 2027, Math 480B: Graphs and Networks

This course will focus on the structure of graphs and networks.  Networks have become an integral part of modern life (Social networks, Biological networks, Transportation networks, ...) and there is a specific branch of mathematics specifically tailored to analyzing which points of the network are central, which points are outliers, which connections vital and which are unimportant.  Other topics include community detection (findinding sub-communities within the network), the structure of random networks models and applications in a variety of different fields.
Prerequisites: minimum grade of 2.0 in MATH 208 and MATH 300

Graduate Special Topics 2026-2027

NOTE: courses are restricted to current Mathematics graduate students or those who have completed a minimum of three 500-level core math courses.  If you have questions about this enrollment requirement visit our page about registering for 500-level courses.

581 C: Uhlmann - Introduction to Inverse Problems and PDE

Introduction to Inverse Problems and PDE

This  is  an introductory course to inverse problems for partial differential equations (PDE).  In these problems one attempts to determine the coefficient or coefficients  of  a PDE by making some measurements of the solutions .
A typical example is when the measurements are made at the boundary of some domain.. Inverse problems have applications in many fields, like medical imaging, physics geophysics, material science, biology, etc.

No previous knowledge of PDE or inverse problems is necessary. We will develop both in the class.

Prerequisite. One can take Math 526 concurrently.

582 A: Alper- Stacks

We will introduce the foundations of stacks with applications to moduli problems.  We will discuss topological and differentiable stacks, but the primary focus will be on algebraic stacks and their use to study moduli problems in algebraic geometry.

Prerequisites: Scheme theory (recommended)

582 B: Yuan - Theory of Linear and Nonlinear Second Order Elliptic Equations

 Linear Theory: Solvability, a priori estimates, Schauder and Calderon-Zygmund estimates, and regularity
   Nonlinear Theory: De Giorgi-Nash-Moser theory for divergence equations (eg. minimal surface equation), Krylov-Safonov theory for nondivergence equations (eg. Monge-Ampere equation [potential equation for maximal gradient graphs/optimal transport], special Lagrangian equation [potential equation for minimal gradient graphs], Bellman equation, and Isaacs equation [optimal stochastic control equations]).
   
   Contents: Harmonic functions (properties), Schauder for △, Weighted norm, solvability for Laplace, Boundary Schauder, L^{p} for △, Energy method, capacity, Poincare, Soblev, W^{1,2} or H¹ space, trace; De Giorgi/Nash, Harnack, Quick applications of Harnack, Minimal surface equations, Viscosity solutions to Nondivergence equations, Alexandrov maximum principle, Krylov-Safonov, Uniqueness and Existence of viscosity solutions, C^{1,α} regularity, C^{2,α} regularity for convex equations, Monge-Ampere and special Lagrangian equations, Bellman equation, and Isaacs equation.
   
   Prerequisites: Advanced calculus/Real Analysis (No previous PDE knowledge is required)

582 C: Liu, G - Modern Matroid Theory

This class will cover matroid theory focusing on developments from the last decades and connections to other areas of mathematics, such as convex geometry and algebraic geometry. Possible topics include the polyhedral perspective on matroid theory, log-concavity inequalities, and permutohedral varieties. 

Prerequisites: linear algebra and abstract algebra

582 D: Pstragowski - Motivic Cohomology

This course would be an introduction to motivic cohomology as constructed by Voevodsky. This is a cohomology theory of smooth schemes obtained by looking at algebraic cycles and the ways they intersect, and it is closely related to algebraic K-theory and special values of L-functions. This course will be a gentle introduction to this circle of ideas, assuming basic familiarity with algebraic geometry and homological algebra. 

583 A: Rothvoss - Lattices

A lattice is discrete subgroup of R^n. Lattices are fundamental objects in discrete math with
a rich set of applications to theoretical computer science, optimization and cryptography.
We will see the following in this course: 
* Introduction to lattices
* Algorithms for the Closest Vector problem
* The Transference Theorems of Banaszczyk
* Khintchine's Flatness Theorem
* Lenstra's algorithm for Integer programming in fixed dimension
* Lattice problems in NP intersected coNP
* The Reverse Minkowski Theorem
* Subspace flatness and the conjecture of Kannan and Lovasz

Prerequisites: A good understanding of convex geometry, probability and algorithms will be very helpful.

 

 583 B: Zhang - Algebraic Operads

We will cover some basics about algebraic operads, definitions, examples, Koszul duality, and quotient operads. Reference book: ``Algebraic Operads'' by Jean-Louis Loday and Bruno Vallette.

 

 

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