Abstract: Ricci flow has been extensively studied, and most results are either specific to dimension 3 or valid in any dimension. However, given the potential topological applications, a theory specific to the 4-dimensional situation is desirable. In this discussion, I will present tools and techniques that are unique to the dimension 4.

Together with A. Deruelle, we introduce a notion of stability for orbifold singularities. This notion helps to explain the formation of orbifold singularities along Ricci flow and lets us construct large classes of ancient Ricci flows. In collaboration with K. Naff, we utilize self-duality in dimension 4 to simplify the evolution equations of curvature. Among other things, this approach lets us to uncover intriguing links between Ricci flow and Yang-Mills flow.

https://math.mit.edu/directory/profile?pid=2272

Computability Theory on Polish Metric Spaces

Doctoral field of study: Mathematics

TBA

Fermat's Last Theorem says the equation \(x^n + y^n = z^n\) has no solution in positive integers when \(n \geq 3\).
This problem was posed by Fermat in the 1600s and a proof of it was announced by Andrew Wiles 30 years ago, on June 23, 1993. This news made the top of the front page of the New York Times, which is quite unusual for an article on mathematics.

In this meeting, we'll watch a documentary about this problem that features Wiles, his colleagues, and other mathematicians whose work played a role in the resolution of Fermat's Last Theorem.


Before the documentary there will be a brief presentation about the link between Fermat's Last Theorem and
elliptic curves, which was the topic of last week's math club meeting.


Note: Free refreshments.

The Loewner energy for Jordan curves is first introduced as the action functional of Schramm-Loewner evolution (SLE), a family of random fractal curves modeling interfaces in 2D statistical mechanics. On the other hand, we show that the Loewner energy coincides with the universal Liouville action introduced by Takhtajan and Teo, which is a Kahler potential for the Weil-Petersson metric on Universal Teichmueller space. This unexpected link suggests that more geometric structures are hidden underneath the probabilistic theory of SLE. I will give an overview of the link between SLE and Kahler geometry of Universal Teichmuller space and a first glimpse into the territory the link has opened up to.

One of the major concerns of the study of reverse mathematics is determining the axiomatic strength of theorems. The focus of this talk is to discuss the axiomatic strength of a particular set of principles,
namely, what will be referred to as “maximal subfamily principles,” which assert the existence of a
maximal subfamily for which a particular \(\Sigma_0^1\) property holds for any pair of sets in the family. It has
already been shown that the addition of the 2 Intersection Principle (which states that every nontrivial family of sets has a maximal subset for which the intersection of each pair of sets is nonempty) to RCA\(_0\) (the subsystem of computable mathematics) is strictly stronger than RCA\(_0\) on its own. Since the 2 Intersection Principle (2IP) is itself a maximal subfamily principle defined by a \(\Sigma_0^1\) property, a natural question that arises is whether there is a principle of this type with a strength strictly above or between RCA\(_0\) and 2IP or if the strength of each maximal subfamily principle of this type is equal to either that
of RCA\(_0\) or 2IP.

To find the most efficient shape of a noise-absorbing wall to dissipate the acoustical energy of a sound wave, we consider a frequency model described by the Helmholtz equation with damping on the boundary modeled by a complex-valued Robin Boundary condition. We introduce a class of admissible Lipschitz boundaries, in which an optimal shape of the wall ensures the infimum of the acoustic energy. Then we also introduce a larger compact class of (ε, ∞) - or uniform domains with possibly non-Lipschitz (for example, fractal) boundaries in which an optimal shape exists, giving the minimum of the energy. The boundaries are described as the supports of Radon measures ensuring their Hausdorff dimension in the segment [n−1, n) . A byproduct of our proof is that the class of bounded (ε, ∞) -domains with fixed ε is stable under Hausdorff convergence. Another related result is the Mosco convergence of Robin-type energy functionals on converging domains.

Abstract: The classical Aviles-Giga functional is a second order energy functional that models phenomena from thin film blistering to smectic liquid crystals. In this talk we will discuss a generalized Aviles-Giga functional in 2D that was first studied by Bochard and Pegon. The zero set of the potential in this generalized functional is a strictly convex $C^1$ submanifold with certain symmetry, instead of $\mathbb{S}^1$ in the classical case. Among other things, we generalize the notion of entropies, and use this tool to establish compactness for sequences with bounded energy and regularity for finite energy states. Our regularity result is also closely related to regularity of finite entropy solutions for a class of scalar conservation laws in 1D. This is joint work with Xavier Lamy and Andrew Lorent.

https://www.wpi.edu/people/faculty/gpeng

TBA

TBA

Note: Free refreshments. The talk starts at 5:40.

TBA

TBA

Thesis topic: Retirement Financial Planning with Basic Expenses Model

Ph.D. in Mathematics with Thesis in Actuarial Science

https://www.math.columbia.edu/~johne/

The Seshadri constants of vector bundles are important local positivity invariants. We compute them for tangent bundles of toric varieties. In particular we confirm the toric case of a conjecture of Fulger and Murayama.

If you are considering graduate school in mathematics or related areas after college, come to this panel discussion where you will hear from members of the UConn math department about their experiences planning for and applying to graduate school. The discussion will then be opened to answer your questions. A packet containing a suggested reading list and some general advice will be provided too.


Note: Free refreshments. The event starts at 5:40.

Join us in the Logic Colloquium for a talk by Liesbeth De Mol!

Detail t.b.a.

https://logic.uconn.edu/calendar/

TBA

TBA

Speaker: Sanjay Ramassamy
(Université Paris-Saclay)

TBA

TBA

Join us in celebrating our undergraduate and graduate students' achievements this year! A small reception for will be held at 3:30pm, and then the award ceremony will begin at 4:00pm.

https://nms.kcl.ac.uk/zoe.wyatt/

Speaker: Beatrice de Tiliere
(University Paris Dauphine)

Abstract: TBA

https://www.physics.ucsb.edu/people/aaron-kennon