This Week in Mathematics


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Today:

Topology seminar
A cyclic version of the generalized S-construction
    - Julie Bergner, University of Virginia
Time: 3:05PM Room: LOV232
Abstract/Desc: A key example of 2-Segal spaces, or decomposition spaces, is the output of Waldhausen's S-construction when applied to an exact category. In joint work with Osorno, Ozornova, Rovelli, and Scheimbauer, we showed that this construction can be generalized to obtain an equivalence of homotopy theories; the most general input is that of an augmented stable double Segal space. Because many interesting examples of 2-Segal spaces additionally have a cyclic structure, a natural question is how to characterize which of these input structures correspond to cyclic 2-Segal spaces. In ongoing joint work with Stern, we are developing such a characterization.

Applied and Computational Math Seminar
The Data Bottleneck in Neural Operators for Engineering Systems: Challenges and Paths Forward
    - Teeratorn Kadeethum, Siemens Energy
Time: 3:05pm Room: 231
Abstract/Desc: Neural operators such as DeepONet and Fourier Neural Operators have shown remarkable promise in learning solution mappings for parametric partial differential equations, offering orders-of-magnitude speedups over traditional solvers. However, their deployment in real engineering systems faces a fundamental chicken-and-egg problem: training these data-hungry models demands large, high-fidelity datasets that are precisely what engineering applications struggle to provide. In practice, experimental measurements are expensive, sparse, and often limited to a handful of observable quantities — for instance, only a few discrete temperature readings may be available in a low-pressure turbine environment, while velocity and pressure fields remain entirely unobservable. High-fidelity simulations can in principle fill these gaps, but they carry their own burdens: long turnaround times, high computational cost, and persistent difficulties in calibration against complex real-world geometries. This talk examines the tension between the data requirements of modern operator learning and the realities of engineering data acquisition, and discusses emerging strategies — including physics-informed training, multi-fidelity fusion, transfer learning, and hybrid simulation-measurement frameworks — for charting a viable path forward.

    - Sam Ballas, FSU
Time: 3:05PM Room: LOV 232

Entries for this week: 12

Monday March 02, 2026

Stochastic Computing
Data Assimilation Framework for Uncertainty Reduction in Learning Data-Driven Dynamical Systems
- Jingqiao Tang, Florida State University
Time: 3:05pm Room: LOV232
Abstract/Desc: Data assimilation (DA) plays a central role in forecasting and decision-making across a range of scientific and engineering disciplines, from geophysics and climate modeling to fluid dynamics and power systems. As data sources become more diverse and system dynamics more complex, traditional DA methods face limitations in scalability, robustness, and the ability to accurately characterize uncertainty. This minisymposium aims to explore recent advances at the intersection of generative artificial intelligence (AI), along with other emerging AI methods, and data assimilation. In particular, we focus on the use of generative models—such as diffusion models, variational autoencoders (VAEs), generative adversarial networks (GANs), and normalizing flows – to enhance the representational power and adaptability of DA frameworks. Topics of interest include, but not limited to, generative modeling for uncertainty quantification, ensemble filtering methods, hybrid physics-informed and data-driven assimilation methods, and novel training-free or low-data approaches. The session will bring together researchers developing theory, algorithms, and applications that leverage generative AI to address challenges in high-dimensional, nonlinear, and partially observed systems.

PhD Defense
Solving Third and Fourth Order Linear Difference Equations in Terms of Second Order Equations.
- Heba Bou KaedBey, FSU
Time: 10:10 Room: LOV 353
Abstract/Desc: Classifying order three and four linear difference operators over C(x) that are solvable in terms of lower order difference operators. In this talk, I will briefly explain how Difference Galois theory helps us in proving the completeness of those classifications. I also discuss the algorithms we developed in Maple for the order three and four cases.

Applied and Computational Math Seminar [url]
Beyond the Resume: How to Get Hired in Competitive Industries
- Teeratorn Kadeethum, Siemens Energy
Time: 3:05pm Room: 101

Tuesday March 03, 2026

Topology seminar
A cyclic version of the generalized S-construction
- Julie Bergner, University of Virginia
Time: 3:05PM Room: LOV232
Abstract/Desc: A key example of 2-Segal spaces, or decomposition spaces, is the output of Waldhausen's S-construction when applied to an exact category. In joint work with Osorno, Ozornova, Rovelli, and Scheimbauer, we showed that this construction can be generalized to obtain an equivalence of homotopy theories; the most general input is that of an augmented stable double Segal space. Because many interesting examples of 2-Segal spaces additionally have a cyclic structure, a natural question is how to characterize which of these input structures correspond to cyclic 2-Segal spaces. In ongoing joint work with Stern, we are developing such a characterization.

Applied and Computational Math Seminar
The Data Bottleneck in Neural Operators for Engineering Systems: Challenges and Paths Forward
- Teeratorn Kadeethum, Siemens Energy
Time: 3:05pm Room: 231
Abstract/Desc: Neural operators such as DeepONet and Fourier Neural Operators have shown remarkable promise in learning solution mappings for parametric partial differential equations, offering orders-of-magnitude speedups over traditional solvers. However, their deployment in real engineering systems faces a fundamental chicken-and-egg problem: training these data-hungry models demands large, high-fidelity datasets that are precisely what engineering applications struggle to provide. In practice, experimental measurements are expensive, sparse, and often limited to a handful of observable quantities — for instance, only a few discrete temperature readings may be available in a low-pressure turbine environment, while velocity and pressure fields remain entirely unobservable. High-fidelity simulations can in principle fill these gaps, but they carry their own burdens: long turnaround times, high computational cost, and persistent difficulties in calibration against complex real-world geometries. This talk examines the tension between the data requirements of modern operator learning and the realities of engineering data acquisition, and discusses emerging strategies — including physics-informed training, multi-fidelity fusion, transfer learning, and hybrid simulation-measurement frameworks — for charting a viable path forward.

- Sam Ballas, FSU
Time: 3:05PM Room: LOV 232

Wednesday March 04, 2026

Biomath Seminar
Inferring Lineage Trees from DNA Barcodes / TBA
- Ashwin Rajendran / Mansura Mome, FSU
Time: 3:05 Room: Love 232
Abstract/Desc: Rajendran: Phylogenetic reconstruction is the process of piecing together possible evolutionary histories of organisms based on their genetic or physical similarities. In recent decades, this strategy has gained popularity in studying mammalian development. Here, the focus is on revealing the developmental tree underlying cell differentiation using the genetic characteristics of developed cells. In this talk, I introduce the concept of lineage tree inference in developmental biology, and present a model for the inference of such trees using a maximum likelihood approach. Mansura: TBA

Biomath lab meetings
Generalization of Complemented Rings
- James Branca, FSU
Time: 2:00 Room: LOV102
Abstract/Desc: It is well known that all complemented rings are reduced. Here we generalize the notion of complemented rings to rings that are not necessarily reduced. We then determine how our concepts fit in with other well-known classes of rings.

Doctoral Defense
Neural Encoding of Taste and Temperature: Single-Neuron and Population Analyses in Gustatory Cortex
- Audrey Nash, FSU
Time: 11:15 Room: 112 KLB
Abstract/Desc: Flavor perception arises from the integration of multiple oral sensations, including taste and temperature, during active ingestion, yet how these signals are represented in the brain remains unclear. In this talk, I will present work showing that gustatory cortex encodes these signals through coordinated patterns of neural activity: single neurons use a combination of firing rate and spike timing relative to the lick cycle to carry complementary information about both taste and temperature, while population-level analyses reveal that the topology of ensemble activity can reliably distinguish sensory conditions even when individual neurons are weakly selective. To interpret population-level activity, we used a spike train metric in our topological analyses that can be framed in terms of optimal transport, providing a principled way to link neural comparisons across scales. Together, this work highlights how cortical circuits integrate multimodal sensory signals and offers new tools for understanding the structure of neural representations in complex behaviors.

Thursday March 05, 2026

Financial Math
Long-Only Minimum-Variance Optimization: Analytical Foundations, Asymptotic Estimation, and the Enhanced Active-Set Algorithm
- Ololade Sowunmi,
Time: 3.05 Room: LOV 231
Abstract/Desc: This dissertation develops a unified theoretical and algorithmic framework for the long‑only minimum variance (LOMV) portfolio problem under a one-factor covariance structure. The work begins by deriving an explicit closed‑form solution to the classical LOMV problem under this structure, providing a complete analytical characterization of the optimal weights and the associated active set. Building on this foundation, we investigate the impact of factor‑loading estimation in high dimensions on the LOMV problem.

Algebra seminar
Cellular A^1-Homology of Smooth Toric Varieties
- Haoyang Liu, UCSB
Time: 3:05pm Room: Zoom
Abstract/Desc: In this talk, we explore the calculations of cellular A^1-homology for smooth toric varieties, an analog of classic cellular homology. We provide an explicit description of pure shellable cases and discuss the derivation of the (Milnor-Witt) motivic decomposition for these cases, inspired by classic results in real toric manifolds. These findings offer new and refined algebraic invariants for toric varieties, reflecting both their complex and real points. Additionally, we present several applications of this computation. This is a joint work with Keyao Peng.

Friday March 06, 2026

Mathematics Colloquium [url]
Leaderless Decisions and Resource Exchange in Collective Foraging
- Zachary Kilpatrick, University of Colorado Boulder
Time: 3:05 Room: Lov 101
Abstract/Desc: Social insects routinely make effective collective decisions and distribute resources without leaders or centralized control, even in uncertain and time-varying environments. This raises a fundamental mathematical question: how can simple, local interaction rules give rise to efficient group-level behavior, and what trade-offs constrain such efficiency? In this talk, I present two complementary models of collective foraging and resource exchange in honeybees. At the decision-making level, I describe a decentralized foraging model in which individuals choose whether to explore or wait under uncertainty while sharing rewards across the group. Stochastic and decision-theoretic analysis shows that efficient collective performance emerges through a division of labor: a small, heterogeneous minority explores, while a synchronized majority commits only when conditions are favorable. At the level of within-hive dynamics, nectar exchange is modeled as a velocity-jump search process coupled to queueing at resource sites, where first-passage and asymptotic analysis reveal how search, congestion, and partial absorption determine scaling laws for resource-exchange cycle times. Together, these results show how leaderless collectives self-organize across scales, balancing efficiency and cost through simple stochastic rules.

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Department of Mathematics

This Week in Mathematics