This Week in Mathematics


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Today:

Financial Math
Principal-agent problem: abstraction and rigor
- Arash Fahim,
Time: 3.05 Room: LOV 231
Abstract/Desc: We review the advances in mathematical formulation of continuous-time principle-agent problem in the recent decade and provide a template for writing agency problems in a rigorous fashion. We present this results in the context of agency problem with effort and agency problem with information asymmetry.

Algebra seminar
Formal groups of elliptic curves
- Amod Agashe, FSU
Time: 3:05pm Room: LOV 232
Abstract/Desc: In this two talk series, we will start by recalling elliptic curves and give the explicit construction of the formal group associated to an elliptic curve. While the construction is explicit, it does not make it clear if the construction is a special case of something more general. We will then describe the formal group of a specific Lie group as motivation for the notion of a formal group, and show the analogy with the case of elliptic curves. After that (most likely in the second talk) we will describe the general abstract construction of the formal group associated to an algebraic group (which includes elliptic curves), and then explain how the explicit construction of the formal group of an elliptic curve described earlier is a special case of this more general construction. Finally, we will explain how a perhaps better way of looking at a formal group is via the formal group scheme associated to an elliptic curve. We will assume background in basic algebraic geometry (e.g., local rings of varieties), but nothing beyond that. The talk is mostly expository in nature, and there will be some interesting algebraic geometry during the talk.

Entries for this week: 4

Tuesday January 20, 2026

Optimal Transport and Its Metrics: From the Classical Wasserstein Distance to Sliced Approaches
- Rocio Diaz Martin, FSU
Time: 3:05PM Room: LOV 232
Abstract/Desc: The goal of this talk is to introduce the Optimal Transport (OT) problem and touch on different metrics that we can create from it. Our objects will be measures or, more specifically, probability distributions. We will begin with the classical Wasserstein distance, discuss its linearized version (including known results and open questions), and then move toward the so-called Sliced-Wasserstein (SW) metric. The latter is a computationally efficient alternative to the Wasserstein distance, comparing probability measures via their one-dimensional projections ("slices"). In particular, for probability measures supported on a compact set, SW induces a topology equivalent to that of the Wasserstein distance, while being substantially cheaper to compute. Despite this topological equivalence, the geometry can differ significantly: unlike the Wasserstein space, the SW space is not geodesic in general. Indeed, classical SW-type approaches quantify dissimilarity but do not provide an explicit "assignment" between the original measures, making it nontrivial to define analogues of Wasserstein "displacement interpolations". This motivates projection-based constructions guided by two questions: can one recover a meaningful transport plan within the sliced framework, and can such constructions yield metrizations with good topological behavior relative to the Wasserstein distance?

Wednesday January 21, 2026

Mathematics Colloquium [url]
Singularity analysis in mean curvature flow
- Wenkui Du, MIT
Time: 3:05 Room: Lov 101
Abstract/Desc: In this talk, I will discuss the singularity theory of mean curvature flow. As the most natural evolution equation in extrinsic geometry, mean curvature flow has striking applications in geometry, topology and image processing. A central challenge for these applications is understanding the structure of singularities. This talk surveys recent progress on the classification of singularity models of mean curvature flow and their applications. In particular, ancient noncollapsed solutions naturally arise when we consider blow-up limits near singularities. Several results about classification of ancient noncollapsed solutions will be presented. I will also mention my future plan of singularity analysis in geometric variational problems. The talk is based on my joint works with collaborators B. Choi, Daskalopoulos, Haslhofer, Sesum, Zhao and Zhu.

Thursday January 22, 2026

Financial Math
Principal-agent problem: abstraction and rigor
- Arash Fahim,
Time: 3.05 Room: LOV 231
Abstract/Desc: We review the advances in mathematical formulation of continuous-time principle-agent problem in the recent decade and provide a template for writing agency problems in a rigorous fashion. We present this results in the context of agency problem with effort and agency problem with information asymmetry.

Algebra seminar
Formal groups of elliptic curves
- Amod Agashe, FSU
Time: 3:05pm Room: LOV 232
Abstract/Desc: In this two talk series, we will start by recalling elliptic curves and give the explicit construction of the formal group associated to an elliptic curve. While the construction is explicit, it does not make it clear if the construction is a special case of something more general. We will then describe the formal group of a specific Lie group as motivation for the notion of a formal group, and show the analogy with the case of elliptic curves. After that (most likely in the second talk) we will describe the general abstract construction of the formal group associated to an algebraic group (which includes elliptic curves), and then explain how the explicit construction of the formal group of an elliptic curve described earlier is a special case of this more general construction. Finally, we will explain how a perhaps better way of looking at a formal group is via the formal group scheme associated to an elliptic curve. We will assume background in basic algebraic geometry (e.g., local rings of varieties), but nothing beyond that. The talk is mostly expository in nature, and there will be some interesting algebraic geometry during the talk.

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Department of Mathematics

This Week in Mathematics