This Week in Mathematics

Department of Mathematics

This Week in Mathematics


>> Next Week [2026-02-15 - 2026-02-21]	>> Beyond Next Week [2026-02-21+]

<< View Previously Scheduled Events

Current Week [Feb 08, 2026 - Feb 14, 2026]

Today:

Stochastic Computing
Introduction of power grid with a numerical example on feedback control problem with data assimilation
- Ruoyu Hu, Florida State University
Time: 3:05PM Room: LOV 232
Abstract/Desc: Modern power grids are large-scale, chaotic dynamical networks. The operation is challenged by lots of factors such as extreme events and increasing demand of electricity. This talk introduces the power grid setting and the Grid2op/L2rpn simulation framework, then presents a numerical example for studying data assimilation in improving the control of the simulated power grid.

Entries for this week: 8

Monday February 09, 2026

Stochastic Computing
Introduction of power grid with a numerical example on feedback control problem with data assimilation
- Ruoyu Hu, Florida State University
Time: 3:05PM Room: LOV 232
Abstract/Desc: Modern power grids are large-scale, chaotic dynamical networks. The operation is challenged by lots of factors such as extreme events and increasing demand of electricity. This talk introduces the power grid setting and the Grid2op/L2rpn simulation framework, then presents a numerical example for studying data assimilation in improving the control of the simulated power grid.

Tuesday February 10, 2026

Topology seminar
Algebraic vs. holomorphic vector bundles
- Aravind Asok, University of South California
Time: 3:05PM Room: Zoom
More Information
Abstract/Desc: A basic question in complex algebraic geometry is to characterize the ``algebraic'' objects amongst ``holomorphic'' objects, when the two notions make sense, e.g., (cohomology classes, K-theory classes, vector bundles). We will discuss recent progress on this question for vector bundles on smooth affine complex varieties. This talk is based on joint work with Tom Bachmann, Jean Fasel and Mike Hopkins.

Applied and Computational Mathematics
- Bryan Quaife, Florida State University
Time: 3:05 Room: 231

Wednesday February 11, 2026

Biomath Seminar
Transport-Induced Delay in Gene Regulatory Feedback / Social Norms and Coalitions
- Christiana Michael / James Branca ,
Time: 3:05 Room: Love 232
Abstract/Desc: Christiana Michael: Many biological systems use feedback loops to regulate gene expression. Feedback is not instantaneous because signaling molecules take time to travel through the cell. This time delay can strongly affect whether the system settles to a steady state or produces oscillations. In this project, we study a gene regulation model where the gene product y(t) produces a signal that is transported through space, in our case a tube. The signal dynamics are modeled using a transport partial differential equation (PDE), and the returning signal provides delayed negative feedback on the gene. From the PDE model, we obtain a delay τ. We then investigate how increasing the delay can lead to oscillations through a Hopf bifurcation at a critical delay. Finally, we discuss how switching between multiple possible delays may influence the persistence or suppression of oscillations. James Branca: Social norms dictate a large part of human behavior, and much work has been done in various fields (both qualitatively and quantitatively) to describe this phenomenon. There has been recent attention from a game theoretic perspective, but it has all been from a non-cooperative and evolutionary standpoint. This talk will present my working ideas to analyze social norms under a cooperative game theoretic lens.

Thursday February 12, 2026

Financial Math
ADAPTIVE CONTROL AND ONLINE PARAMETER ESTIMATION FOR STOCHASTIC SYSTEMS
- Changkui Wu, FSU
Time: 3.05 Room: LOV 231
Abstract/Desc: We propose a continuous-time online estimator derived from a likelihood-based formulation for stochastic differential equations. The estimator admits a compact stochastic differential representation and incorporates adaptive feedback through a lagged structure, ensuring measurability and well-posedness of the closed-loop system. Under standard regularity and monotonicity assumptions, we establish almost sure and mean-square convergence of the estimator to the true parameter. The convergence proof is based on a Lyapunov framework combined with an integrating factor technique, leading to a three-term decomposition that separates the effects of the initial condition, diffusion noise, and stochastic fluctuations. Importantly, the analysis does not require stationarity of the state process or time-scale separation.

Algebra seminar
The Catalan Numbers
- Ahmer Khan, FSU
Time: 3:05pm Room: LOV 0232
Abstract/Desc: The Catalan numbers form a ubiquitous sequence in combinatorics, counting a rich variety of objects. In this talk, we will explore the fundamental ideas that explain this ubiquity. We first present a classical probability problem from the 'Green Book' where the Catalan numbers arise naturally and then show the first of a few important bijections between the various objects that the Catalan numbers count. We then introduce the basic recurrence and derive the closed-form formula via generating functions. Finally, we present a more elegant solution using the reflection principle for random walks. Time permitting, we will discuss additional distinct 'Catalan' objects and their algebraic and combinatorial significance.

Friday February 13, 2026

Data Science and Machine Learning Seminar [url]
A variational approach to studying dimension reduction algorithms
- Ryan Murray, NC State
Time: 1:20 Room: Lov 101
Abstract/Desc: Dimension reduction algorithms, such as principal component analysis (PCA), multidimensional scaling (MDS), and stochastic neighbor embeddings (SNE and tSNE), are an important tool for data exploration, visualization, and subgroup identification. While these algorithms see broad application across many scientific fields, our theoretical understanding of non-linear dimension reduction algorithms remains limited. This talk will describe new results that identify large data limits for MDS and tSNE using tools from the Calculus of Variations. We'll highlight connections with Gromov-Wasserstein distances, manifold learning, and Perona-Malik diffusion. Along the way, we will showcase situations where standard libraries give outputs that are misleading, and propose new computational algorithms to mitigate these issues and improve efficiency.

Mathematics Colloquium [url]
Analysis and Control in Poroelastic Systems with Applications to Biomedicine
- Lorena Bociu, NC State
Time: 3:05 Room: Lov 101
Abstract/Desc: In biomechanics, local phenomena, such as tissue perfusion, are strictly related to the global features of the surrounding blood circulation. We propose a heterogeneous model where a local, accurate, 3D description of fluid flows through deformable porous media by means of poroelastic systems is coupled with a systemic 0D lumped model of the remainder of the circulation. This represents a multiscale strategy, which couples an initial boundary value problem to be used in a specific region with an initial value problem for the rest of the circulatory system. We present new results on wellposedness analysis, optimal control and solution methods for this nonlinear multiscale interface coupling of PDEs and ODEs. Our results have applications in biomedicine and bioengineering, including tissue perfusion, fluid flow inside cartilages and bones, and design of bioartificial organs.

Problems? Email webmaster@math.fsu.edu.

February