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This Week in Mathematics

>> Next Week [2025-10-19 - 2025-10-25] >> Beyond Next Week [2025-10-25+]
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Today:
Biomath lab meetings
Storm the Field! A PDE approach
    - Jonathan Engle, FSU
Time: 5:30 Room: LOV105
Abstract/Desc: Partial Differential Equations (PDE's) have historically been used to model a variety of physical, ecological and social phenomenon. This talk will first consist of an introduction to PDE's with some classic examples. We then will discuss the social phenomenon of field storming. Field storming is when fans run onto the playing surface after a game, typically to celebrate a major victory or upset. This talk aims to formulate a PDE which will model the social phenomenon of "Field storming/ rushing" via the Aggregation Diffusion model.

Biomathematics Journal Club
Mathematical Modelling of Macrophage and Natural Killer Cell Immune Response During Early Stages of Peritoneal Endometriosis Lesion Onset
    - James Thornham, FSU
Time: 5:00 Room: Dirac Library

Entries for this week: 5
Tuesday October 14, 2025

Applied and Computational Math
A Diffusion Model-Based Data Assimilation Framework for Unvertainty Reduction in Learning Data-Driven Dynamical Systems. 
    - Jingqiao Tang, Florida State University
Time: 3:05pm Room: LOV 306
Abstract/Desc: We present a hybrid data assimilation framework that combines long short-term memory (LSTM) based neural networks with the Ensemble Score Filter (EnSF) for nonlinear dynamical systems. LSTM models provide accurate short-term forecasts, but their performance deteriorates over longer horizons due to error accumulation. To overcome this limitation, observational data are assimilated using EnSF, which updates the ensemble of LSTM forecasts while accommodating nonlinear and non-Gaussian state distributions. Numerical experiments with the 20-dimensional Lorenz 96 system demonstrate that the LSTM–EnSF framework effectively corrects long-term forecast errors and yields robust state estimation, highlighting its promise for improving data-driven prediction in complex dynamical systems. 
Wednesday October 15, 2025

Biomath lab meetings
Storm the Field! A PDE approach
    - Jonathan Engle, FSU
Time: 5:30 Room: LOV105
Abstract/Desc: Partial Differential Equations (PDE's) have historically been used to model a variety of physical, ecological and social phenomenon. This talk will first consist of an introduction to PDE's with some classic examples. We then will discuss the social phenomenon of field storming. Field storming is when fans run onto the playing surface after a game, typically to celebrate a major victory or upset. This talk aims to formulate a PDE which will model the social phenomenon of "Field storming/ rushing" via the Aggregation Diffusion model.
Biomathematics Journal Club
Mathematical Modelling of Macrophage and Natural Killer Cell Immune Response During Early Stages of Peritoneal Endometriosis Lesion Onset
    - James Thornham, FSU
Time: 5:00 Room: Dirac Library
Thursday October 16, 2025

Financial Math
Optimal Fees for Liquidity Provision in Automated Market Makers
    - Steven A. Campbell, Columbia University
Time: 3.05 Room: Zoom
Abstract/Desc: Passive liquidity providers (LPs) in automated market makers (AMMs) face losses due to adverse selection (LVR), which static trading fees often fail to offset in practice. We study the determinants of LP profitability in a reduced-form model where an AMM operates in parallel with a centralized exchange (CEX), traders route their orders optimally to the venue offering the better price, and arbitrageurs exploit price discrepancies. Combining large-scale simulations, tractable theory, and real market data, we analyze how LP profits vary with market conditions such as volatility and trading volume. A key trade-off emerges: fees must be low enough to attract volume, yet high enough to mitigate arbitrage losses. Under normal market conditions, the profit-maximizing AMM fee is competitive with the trading cost on the CEX and remarkably stable, whereas in periods of very high volatility, a high fee protects passive LPs from severe losses. Based on joint work with Philippe Bergault, Jason Milionis and Marcel Nutz.
Algebra seminar
Integral elements and normalization in tropical geometry
    - Kalina Mincheva, Tulane
Time: 3:05pm Room: LOV 0231
Abstract/Desc: This work is part of a broader program to develop necessary commutative algebra tools for the semirings arising from tropicalization. We will discuss different notions of integrality which while equivalent for rings are not for idempotent semirings. We will define integral closure and give different characterizations. If time permits we will give some examples of normalization in tropical geometry.

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