Fall 2025 – Summer 2026 – Abstracts
Friday, Sept 26, 2025. Mathematics Research Seminar.
Prof Evan Miller, University of Maine
Permutation symmetric solutions of the incompressible Euler equation and related models
Neville 421, 3:00 – 4:30pm.
Abstract: In this talk, I will discuss some results for the incompressible Euler equation and related models under permutation symmetry. The Fourier-restricted Euler equation is a model equation for the Euler equation where the Helmholtz projection is replaced by a projection onto a subspace of divergence free vector fields, but the nonlinearity is otherwise unchanged. There are permutation symmetric solutions of the Fourier-restricted Euler equation that exhibit finite-time blowup. This is also true in the viscous case when the fractional dissipation is small enough. I will also discuss some conditional results for the full Euler equation.
Wednesday, Sept. 24, 2025. Mathematics Colloquium.
Prof. Evan Miller, University of Maine
Weak and strong solutions of the Navier-Stokes equation
Hill Auditorium
Refreshments at 3pm; Talk: 3:15 – 4:05 pm.
Abstract: In this talk, I will discuss solutions of the Navier-Stokes equation. I will introduce the concept of a weak solution of a PDE, with a particular focus on the Navier-Stokes equation. I will also discuss scaling properties of the Navier-Stokes equation. The global regularity problem for Navier-Stokes is particularly challenging in three dimensions because of the relationship between scaling and energy.
Friday, Sept 19, 2025. Mathematics Research Seminar.
Prof Jack Buttcane, University of Maine
An update on Bessel functions and minimax problems
Neville 421, 3:00 – 4:30pm.
Abstract: I’ll give an update on two problems I’ve already discussed in the seminar on the GL(n) Bessel functions and a minimax problem related to vector-valued automorphic forms.
Wednesday, Sept. 17, 2025. Mathematics Colloquium.
Prof. Sheela Devadas, University of Maine
Higher-weight Jacobians: Generalizing the idea of adding points on a curve
101 Neville Hall
Talk 3:15 – 4:05 pm, refreshments at 3pm
Abstract: An abelian variety is a geometric object which also has a way to “add” points. One-dimensional abelian varieties, elliptic curves, are important objects in number theory, with applications to cryptography, integer factorization, and primality proving. While we cannot “add” points on a general curve, we can embed any curve over the complex numbers inside a higher-dimensional abelian variety known as the Jacobian.
In this talk I will discuss my work with Max Lieblich, where we generalize the notion of the Jacobian of a complex curve to higher-dimensional varieties and higher “weights”. Jacobians of weight 2 are connected to ideas from number theory such as the Brauer group and Tate conjecture. We use the theory of CM elliptic curves and lattices in the complex numbers to compute certain higher-weight Jacobians as complex tori. Surprisingly, we find that they are always algebraic. However, we can see there is something non-algebraic about the construction by considering the minimal fields of definitions of 2-Jacobians of abelian surfaces.