This Week in Mathematics


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Today:

Biomathematics Seminar
Delay-Induced Degrade-and-Fire Oscillations in Small Genetic Circuits
- Christiana Michael, Rachel Veit-Holt, Zach Deskin, and Afolabi Ariwayo,
Time: 3:05 PM Room: LOV 232

Financial Math Proseminar
Finance Industry Employment Q&A
- Lisa Goldberg, Blackrock and UC Berkeley
Time: 3:05pm Room: LOV 102
Abstract/Desc: An informal Q&A about mathematicians employed as quants in the financial sector. Dr. Goldberg has extensive experience mentoring in the investments world. All interested students are welcome to join us!

Entries for this week: 9

Monday March 24, 2025

Dissertation defense
Topics in intersection theory: algebraic and tropical perspectives
- Franquiz Caraballo-Alba, FSU
Time: 3:30 Room: 204a
Abstract/Desc: This talk will focus on two areas, algebraic geometry and tropical geometry-matroid theory. The unifying theme is the application of intersection theory to both of these branches of geometry. For the first half of the talk, we will define the predegree polynomial of a hypersurface in projective space, an invariant which encodes information about the orbit of a hypersurface under automorphisms of the ambient projective space. We will provide formulae for their computation using different approaches and compute this invariant in the case of nonsingular quadrics in projective 3-space, through the geometry arising from the set up. For the second half, we will derive a compact formula for the Chern-Schwartz-MacPherson (CSM) cycle of a matroid, a generalization of the CSM class of the complement of a hyperplane arrangement, by introducing the staircase class in the Chow ring of a matroid. The main result of this part of the talk is the confirmation of a conjecture of Tara Fife and Felipe Rincón about the shape of the Poincaré dual of the CSM cycle of a matroid.

Tuesday March 25, 2025

Geometry and Topology Seminar [url]
The comical model structures
- Brandon Doherty, FSU
Time: 3:05 Room: 232
More Information
Abstract/Desc: We discuss the comical model structures on the category of marked cubical sets, a family of models for (infinity,n)-categories studied in joint work with Kapulkin and Maehara, building on previous work of Campion-Kapulkin-Maehara. In particular, we focus on the Quillen equivalence between the comical model structures and the complicial model structures on marked simplicial sets via the marked triangulation functor and its right adjoint.

ACM seminar
Pure-quartic solitons with PT-symmetric nonlinearity
- Savvas Sardelis, FSU
Time: 3:05 pm Room: 0231
Abstract/Desc: The idea of having solitary waves in Kerr nonlinear media arising in the presence of only quartic dispersion was briefly theoretically considered in the early 90's and then almost forgotten until its experimental discovery in 2016. These so-called pure-quartic solitons (PQS) were observed in a silicon photonic crystal waveguide where quartic dispersion was the dominant dispersion effect and all the other dispersion orders were negligible. In this talk, we present a new class of soliton based on the interaction of parity-time (PT) symmetric nonlinearity and quartic dispersion or diffraction. This novel kind of soliton is related to the recently discovered PQS, that arises from the balance of Kerr nonlinearity and quartic dispersion, through a complex coordinate shift. We find that the PT-symmetric PQS are linearly stable and present important differences with respect to its Hermitian (Kerr) counterpart, including a nontrivial phase structure, a skewed spectral intensity, and a higher power for the same propagation constant.

Financial Mathematics Seminar [url]
Optimization, Estimation, Geometry
- Lisa Goldberg, UC Berkeley and Blackrock
Time: 3:05 Room: 0101
Abstract/Desc: [NOTE special Tuesday meeting] I will discuss recent results that identify and correct bias in high dimensional eigenvectors. These results rely on geometry and concentration of measure in high dimensions, and have potential applications to machine learning, genomics and signal processing, as well as to problems in portfolio optimization that were introduced in the 1950s by Nobel Laureate Harry Markowitz, who was a graduate student at the time. Markowitz died in 2023 at the age of 95. My work, developed in collaboration with Alec Kercheval, Alex Shkolnik and many others, is dedicated to his memory.

Wednesday March 26, 2025

Biomathematics Seminar
Delay-Induced Degrade-and-Fire Oscillations in Small Genetic Circuits
- Christiana Michael, Rachel Veit-Holt, Zach Deskin, and Afolabi Ariwayo,
Time: 3:05 PM Room: LOV 232

Financial Math Proseminar
Finance Industry Employment Q&A
- Lisa Goldberg, Blackrock and UC Berkeley
Time: 3:05pm Room: LOV 102
Abstract/Desc: An informal Q&A about mathematicians employed as quants in the financial sector. Dr. Goldberg has extensive experience mentoring in the investments world. All interested students are welcome to join us!

Thursday March 27, 2025

Algebra seminar
Rational Torsion in Abelian Varieties Associated to Newforms
- Matthew Winters, FSU
Time: 3:05PM Room: 232
Abstract/Desc: Let f be a weight 2 newform on Γ_0(N) with N square free and A the abelian subvariety of the Jacobian J_0(N) associated to f. We show that if m is an ideal of the Hecke algebra with residue characteristic r not dividing 2N such that A[m] is reducible, then A[m] has a rational point. We discuss some necessary definitions and sketch the method of proof. In particular, we also mention the differences in the case of r = 3.

Friday March 28, 2025

Data Science and Machine Learning Seminar
Dynamic Generative AI for Uncertainty Quantification
- Feng Bao, FSU
Time: 1:20 Room: Lov 106
Abstract/Desc: Generative machine learning models, including variational auto-encoders (VAE), normalizing flows (NF), generative adversarial networks (GANs), diffusion models, have dramatically improved the quality and realism of generated content, whether it's images, text, or audio. In science and engineering, generative models can be used as powerful tools for probability density estimation or high-dimensional sampling that critical capabilities in uncertainty quantification (UQ), e.g., Bayesian inference for parameter estimation. Studies on generative models for image/audio synthesis focus on improving the quality of individual sample, which often make the generative models complicated and difficult to train. On the other hand, UQ tasks usually focus on accurate approximation of statistics of interest without worrying about the quality of any individual sample, so direct application of existing generative models to UQ tasks may lead to inaccurate approximation or unstable training process. To alleviate those challenges, we developed several new generative diffusion models for various UQ tasks, including a score-based nonlinear filter for recursive Bayesian inference, and a training-free ensemble score filter for tracking high dimensional stochastic dynamical systems. We will demonstrate the effectiveness of those methods in various UQ tasks including tracking high-dimensional Lorenz 96 systems and data assimilation for multiple geophysical models.

Mathematics Colloquium [url]
Lehmer's number in Topology, Geometry and Dynamics
- Eko Hironaka, Emeritus Professor at Florida State University
Time: 3:05 Room: 101
Abstract/Desc: A Salem number is an algebraic integer s with the property that all roots of its minimal polynomial P(x) besides s and 1/s have complex norm equal to one (i.e. lie on the unit circle). In 1933, after extensive computer search, Lehmer asked whether the larger real root of P(x) = x^10 + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1 (roughly 1.17625) is the smallest Salem number. The problem is still open. Lehmer's query has led to an on-going study of deep relations between number theory, and the study of the topology, geometry and dynamical properties of a variety of mathematical objects. In this talk we will discuss some results in these directions that have come to light in recent decades involving knot theory, hyperbolic geometry, Coxeter theory, and the dynamics of rational maps.

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Department of Mathematics

This Week in Mathematics