Colloquium Coordinator: Debraj Chakrabarti (Fall 2026: C-Y. Jean Chan)
Because there might be a time delay in updating the webpage, please always check with the Coordinator for the available dates.
Typical Colloquium Talks are Thursday, 4:00–4:50pm, in person in Room 227 of Pearce Hall.
Special media arrangement such as virtual, or HyFlex format, if available,
is indicated under Remark.
The following table gives the information for all colloquium activities (on any day), and each Thursday event that is open to the public.
For Graduate Student Seminar (GSS) schedule on Tuesdays, please click here.
| Date | Speaker | Title (Scroll down for Abstract) | Remark | 9/24/2026 | Ben Savoie (Peking University, China) | From Elliptic Curves to Graph Theory: The Four Color Theorem and Rank-Zero Curves |
|---|---|---|---|
| 10/1/2026 | Department Meeting | 10/8/2026 | Zhiliang Xu (University of Notre Dame) | TBD | 10/16/2025 | Mark Iwen (MSU) | Sparse Spectral Methods for Solving High-Dimensional and Multiscale PDEs | 10/22/2026 | 10/29/2026 | 11/05/2026 | Department Meeting | 11/12/2026 | 11/29/2026 | 11/26/2026 | Thanksgiving | Have a Thankful and Warm Holiday | 12/03/2026 | Department Meeting | 2027 | Spring Semester | To Be Continued |
Speaker: Ben Savoie (9/24/2026) (Beijing International Center for Mathematical Research, Peking University, China)
Title: From Elliptic Curves to Graph Theory: The Four Color Theorem and Rank-Zero Curves
Abstract:
What does the Four Color Theorem have to do with solving cubic equations? In this talk, we begin with the classical problem of finding rational points on elliptic curves and the remarkable addition law that gives these points the structure of a finitely generated group. One of the central invariants of an elliptic curve is its rank, which measures the number of independent infinite-order rational points, but determining it is typically very difficult.
For elliptic curves of the form y² = x³ + bx over the Gaussian rationals Q(i), we will see how this arithmetic problem can be translated into graph theory. The vertices of the graph correspond to prime factors of b, while its edges encode quadratic-residue relations between those primes. The resulting graph and its binary Laplacian describe a Selmer group associated to the curve, giving an upper bound for its rank.
This single graph in fact controls an entire family of elliptic curves obtained by varying which prime factors appear in b. As an application, we will see how the Four Color Theorem can be used to construct large collections of rank-zero elliptic curves, each having only finitely many rational points.
No prior knowledge of elliptic curves, Selmer groups, or graph theory will be assumed.
Speaker: Zhiliang Xu (10/8/2026)
Title: TBD
Abstract:
TBD
Speaker: Mark Iwen (10/15/2026)
Title: Sparse Spectral Methods for Solving High-Dimensional and Multiscale PDEs
Abstract:
In this talk we discuss sparse spectral methods capable of rapidly and automatically determining a set of Fourier basis functions whose span is guaranteed to contain an accurate approximation of the solution of a given PDE on a (potentially very high-dimensional) periodic domain. This small, near-optimal Fourier basis is then used to efficiently solve the given PDE in a runtime which only depends on the PDE’s data compressibility properties, while breaking the curse of dimensionality and relieving linear dependence on any multiscale structure in the original problem. Convergence analysis in the Sobolev norm for a general class of non-constant diffusion equations will be discussed in the elliptic setting, as well as initial attempts to extend the methods to related parabolic PDE. Numerical experiments will demonstrate good empirical performance on several multiscale and high-dimensional example problems, showcasing the promise of the proposed methods in practice.
This talk will draw on joint work with various subsets of Craig Gross/Grosch (MSU) and Tanvi Mahajan (MSU)
Speaker: TBD
Title: TBD
Abstract:
TBD