Schedule of Prior Academic Years

Spring 2026

• 01/16/2026
  Organizational Meeting

• 01/23/2026 -- UF-FSU Geometry and Topology Meeting
  No Seminar talk

• 01/30/2026
  Speaker: Shu Liu (FSU)
  Title: A generative approach for simulating Wasserstein geometric flows

Abstract: Wasserstein geometric flows (WGFs) constitute a class of time-evolution partial differential equations that play a fundamental role in modeling and simulating physical systems. In this talk, we present a sampling-friendly, optimization-free approach for simulating WGFs by leveraging generative models from deep learning. Specifically, we project the WGF defined on the probability manifold onto a finite-dimensional parameter space induced by the generative model, in a manner that faithfully mimics the dynamics of the original geometric flow. The resulting system of ordinary differential equations, referred to as the parametrized WGF, can then be efficiently solved using classical numerical integration methods. This framework enables direct generation of samples from the time marginals of the WGFs, even in high-dimensional settings. In addition, we establish error analysis that provides accuracy guarantees for the proposed method. The talk will conclude with a brief discussion of future research directions and potential applications.

• 02/06/2026
  Speaker: Eric Kubischta (FSU)
  Title: Finding Your Inner Qubit  — Quantum Computing 101

Abstract: Quantum computing has a reputation for being mysterious, but the basic model is simple: quantum states are complex vectors, gates are unitary matrices, and measurement produces random outcomes with probabilities determined by squared inner products. This talk introduces qubits and quantum circuits with minimal physics, using the Bloch sphere (the complex projective line CP^1) as a visual aid for single-qubit states, gates, and measurements. We will discuss why we need quantum mechanics at all, what is meant by a “quantum speedup,” and highlight a few canonical quantum algorithms that achieve provable advantage over classical algorithms. We will also cover the main obstacles to building large-scale quantum computers today, and time permitting, we will outline what “quantum machine learning” usually refers to and why practical advantages remain an open question.

• 02/13/2026 -- Joint Seminar with the FSU-NC State PDE Day and with the SC Artificial Intelligence Seminar 
  Speaker: Ryan Murray (NC State)
  Title: A variational approach to studying dimension reduction algorithms 

Abstract: 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.

• 02/20/2026
  Speaker:  Ferhat Karabatman  (FSU)
  Title: Geometric Perspective on Concentration Phenomena in Frame Theory
  Abstract: Frames are fundamental structures in many areas, and tight frames are particularly valued for their stability and robustness properties. In this work, we establish concentration phenomena for Parseval frames, i.e. tight frames with frame bound 1, under isotropic distributions supported on the sphere and the Euclidean ball, showing that epsilon-nearly Parseval frames are prevalent in these probabilistic models. We further introduce a distinguished subclass of Parseval frames and prove that they are both robust under the Bernoulli-type erasure model and prevalent within the space of Parseval frames. As an application of our results, we derive a high-probability upper bound of order o(epsilon d) for the Paulsen problem.

• 02/27/2026 (Zoom Talk)
  Speaker: Javier Gómez-Serrano (Brown)
  Title: Mathematical Exploration and Discovery at Scale
  Abstract: Machine learning is transforming mathematical discovery, enabling advances on longstanding open problems. In this talk, I will discuss AlphaEvolve, a general-purpose evolutionary coding agent that uses large language models to autonomously discover old and new mathematical constructions and potentially go beyond them. AlphaEvolve tackles a wide variety of problems across analysis, geometry, combinatorics, and number theory. In some instances, AlphaEvolve is also able to generalize results for a finite number of input values into a formula valid for all input values. Furthermore, we are able to combine this methodology with Deep Think and AlphaProof in a broader framework where the additional proof-assistants and reasoning systems provide automated proof generation and further mathematical insights. This illustrates how general-purpose AI systems can systematically successfully explore broad mathematical landscapes at an unprecedented speed, leading us to do mathematics at scale.

• 03/13/2026
  Speaker: Rafiq Islam (FSU)
  Title: Decentralized Constrained Sampling via Proximal Stochastic Langevin Dynamics
  Abstract: We propose Decentralized Proximal Stochastic Gradient Langevin Dynamics (DPSGLD), a novel algorithm for constrained sampling over multi-agent networks. In this framework, agents process local data subsets and communicate only with neighbors to jointly sample from a posterior distribution supported on a compact convex set. We handle constraints using a shared proximal regularization via the Moreau–Yosida envelope, which enables unconstrained stochastic updates that approximate the target Gibbs distribution. We establish non-asymptotic convergence guarantees in the 2-Wasserstein distance for both individual iterates and the network average, explicitly characterizing the effects of network topology, gradient noise, and regularization bias. Experimental results on Bayesian linear and logistic regressions demonstrate that DPSGLD achieves faster posterior concentration and higher predictive accuracy than centralized SGLD. We further show that performance scales positively with increased network connectivity, confirming the algorithm’s efficiency for distributed Bayesian learning.

• 03/27/2026 -- Special Session on Geometric Methods for Data Science at the 2026 Spring Southeastern Sectional Meeting
  No Seminar talk

• 04/03/2026-- Joint Seminar with the SC Artificial Intelligence Seminar   
  !!!Special Location and Time: 499 Dirac Science Library at 12:00pm!!!
  Speaker:  Zavala Romero group (FSU Scientific Computing)
  Title: AI for Scientific Discovery
  Abstract: This talk examines how machine learning and artificial intelligence are being used not only in healthcare applications, but also as tools for scientific discovery in biomedicine and medicine. It traces the field from early predictive models and image-based deep learning to modern foundation models, multimodal systems, and AI-enabled software used in clinical and research settings. Rather than focusing on heavy mathematics, the emphasis is on how these methods support discovery, hypothesis generation, pattern finding, and decision-making across biological, medical, and healthcare data.

• 04/10/2026
  Speaker:  Pan Fang (FSU)
  Title: Multiparameter persistence landscapes
  Abstract: Persistent homology studies the evolution of homological features across a filtration. In the one-parameter setting, barcodes provide a simple and powerful summary. Multiparameter persistence is more complicated, and unlike in the one-parameter setting, there is no direct barcode analogue in general. Multiparameter persistence landscapes offer one approach to understanding this richer setting. In this talk, we introduce the directional persistence landscape and integrated persistence landscape. We study metric properties among them and present stability and instability results, including results related to the erosion distance and the interleaving distance. We also show that the interior of the landscape interval is determined by finitely many points, and describe the general form of the integrated landscape curves.

• 04/17/2026
  Speaker:  Washington Mio (FSU)
  Title: The Observable Wasserstein Distance
  Abstract: Calculating the Wasserstein distance between large point clouds in metric spaces is computationally costly. In Euclidean space, the sliced Wasserstein distance provides a more accessible alternative. We develop an analogue of slicing techniques for probability measures or data in metric spaces to obtain a computationally more tractable lower bound for the Wasserstein distance, a metric that we term observable Wasserstein distance. This is joint work with T. Needham, E. dos Santos, and L. Mauri.

• 04/24/2026
  Speaker:  Mao Nishino FSU)
  Title: Conditioning a measure-valued diffusion on the Wasserstein space
  Abstract: We consider conditioning of the Dirichlet–Ferguson diffusion on the Wasserstein space of probability measures over the torus. Starting from its Dirichlet-form construction and particle representation, we introduce conditioning by a positive terminal functional and show that the resulting law is a Doob h-transform of the original diffusion. The transform is characterized through the solution of a backward heat equation associated with the Dirichlet–Ferguson Laplacian, and a Girsanov argument yields the corresponding drifted particle dynamics. We further study finite-dimensional truncations of this conditioned system, identify their transition families, and prove convergence to the infinite-dimensional conditioned dynamics in the generalized Hilbert sense. We also discuss numerical approximation and present an explicit Gaussian terminal-conditioning example leading to a tractable simulation scheme.

Fall 2025

• 08/29/2025 

Organizational Meeting

• 09/05/2025 -- Remote
  Speaker: Elias Döhrer (TU Chemnitz)
  Title: Incorporating Self-Repulsion into Riemannian metrics

Abstract: Inspired by the work of Michor, Bauer, Bruveris, Maor et al. on the manifold of immersed curves, we propose a new strong Riemannian metric on the manifold of (parametrized) embedded curves of H^s regularity, s in (3/2,2). The construction is motivated by the concept of tangent-point energies, a family of self-avoiding functionals on curves and surfaces of arbitrary dimension. Their notion of self-repulsion allowed us to capture the topological property „embeddedness“ in a continuous way. This talk illustrates the impact of this metric and highlights its most important features, namely metric and geodesic completeness, relative compactness of bounded sets with respect to the weak H^s topology, and existence of length-minimizing geodesics between every pair of curves in the same knot class. https://arxiv.org/abs/2501.16647

• 09/12/2025 

Speaker: Caroline Moosmüller (University of North Carolina at Chapel Hill)
Title: Learning in the space of probability measures

Abstract: Many datasets in modern applications - from cell gene expression and images to shapes and text documents - are naturally interpreted as probability measures, distributions, histograms, or point clouds. This perspective motivates the development of learning algorithms that operate directly in the space of probability measures. However, this space presents unique challenges: it is nonlinear and infinite-dimensional. Fortunately, it possesses a natural Riemannian-type geometry which enables meaningful learning algorithms. This talk will provide an introduction to the space of probability measures and present approaches to unsupervised, supervised, and manifold learning within this framework. We will examine temporal evolutions on this space, including flows involving stochastic gradient descent and trajectory inference, with applications to analyzing gene expression in single cells. The proposed algorithms are furthermore demonstrated in pattern recognition tasks in imaging and medical applications.

• 09/19/2025 -- Joint Seminar with the SC Artificial Intelligence Seminar 

Speaker: Rocío Díaz Martín (FSU) 

Title: The Barycentric Coding Model in Optimal Transport

Abstract: The context of this seminar will be the theory of Optimal Transport and its applications. We will consider the problem of estimating a point, either a distribution or a network, under the Barycentric Coding Model with respect to the Wasserstein (W) or Gromov-Wasserstein (GW) distance functions. Specifically, assuming that the target belongs to the set of W or GW barycenters of a finite collection of known templates, we aim to estimate the unknown barycentric coordinates with respect to those templates. In other words, the goal is to determine the right combination of templates (or barycentric coordinates) that best reconstructs the target. From the perspective of harmonic analysis, computing barycenters can be seen as a 'synthesis problem', whereas retrieving their coordinates corresponds to solving an 'analysis problem'. We will review the general theory for the classical case, i.e., using the Wasserstein metric, and then delve into the Gromov-Wasserstein case. For the latter, we focus on algorithms for finding barycentric coordinates (analysis), leveraging existing techniques for constructing barycenters (synthesis) that rely on fixed-point iteration (G. Peyré, M. Cuturi, and J. Solomon, 2016) and differentiation approaches via a blow-up method (S. Chowdhury and T. Needham, 2020). Applications will include covariance estimation, classification, compression, and data imputation.

• 09/26/2025
  Speaker: Cagatay Ayhan (FSU)

Title: Equivalence of Landscape and Erosion Distances for Persistence Diagrams

Abstract: This talk is based on our recent work arXiv:2506.21488, which establishes connections between three of the most prominent metrics on persistence diagrams in topological data analysis: the bottleneck distance, Patel’s erosion distance, and Bubenik’s landscape distance. Our main result shows that the erosion and landscape distances are equal, thereby bridging the former's natural category-theoretic interpretation with the latter's computationally convenient structure. The proof utilizes the category with a flow framework of de Silva et al., and leads to additional insights into the structure of persistence landscapes. Our equivalence result is applied to prove several results on the geometry of the erosion distance. We show that the erosion distance is not a length metric, and that its intrinsic metric is the bottleneck distance. We also show that the erosion distance does not coarsely embed into any Hilbert space, even when restricted to persistence diagrams arising from degree-0 persistent homology. Moreover, we show that erosion distance agrees with bottleneck distance on this subspace, so that our non-embeddability theorem generalizes several results in the recent literature.

• 10/03/2025
  Speaker: Ali Kara (FSU)

Title: Linear Function Approximations in Reinforcement Learning

Abstract: Control and learning of stochastic dynamical systems suffer from both the curse of dimensionality and the curse of history, since an optimal control generally depends on the entire history of observables.  In this talk, I will talk about the standard approach of linear function approximation for learning in control. We will see that in this setting; the learning algorithms track the composition of an approximate Bellman operator with a projection operator. For policy evaluation, this composition can be shown to be contractive in L_2 norm of the stationary distribution of the finite-memory variables. Consequently, the learning method converges to an estimate that is sufficiently close to the true value of the policy under appropriate conditions.

However, for optimal value estimation, due to the mismatch between the exploration policy and the optimal policy, the learning algorithms, in general, may be unstable except in certain special cases. These special cases include: (i) when the basis functions are orthogonal, (ii) when the output of Bellman operator remains in the span of the basis functions. 

• 10/10/2025
  Speaker: Kun Meng (FSU Statistics)

Title: A Bridge Between Topological and Functional Data

Abstract: In the 21st century, we have seen a growing availability of shape-valued and imaging data, prompting the development of new statistical methods to analyze them. Importantly, bridging the new methods and existing frameworks is advisable. In this talk, I will introduce several statistical inference methods for shapes and images based on the Euler characteristic. These methods have applications in many fields, such as geometric morphometrics and radiomics. From a statistical perspective, these methods are naturally connected to functional data analysis. From a mathematical viewpoint, they are grounded in solid foundations, bridging various branches of mathematics: algebraic and tame topology, Euler calculus, functional analysis, and probability theory. I will also briefly discuss some of my ongoing and future research directions.

• 10/17/2025
  No Seminar this week!

• 10/24/2025 -- Joint Seminar with the SC Artificial Intelligence Seminar   
  !!!Special Location and time: 499 Dirac Science Library at 12:00pm!!!
  Speaker: Gordon Erlebacher (FSU Scientific Computing)

Title: Latest Architectures, Hierarchical Reasoning Model

Abstract: This talk links standard LLM practice to the Hierarchical Reasoning Model (HRM). Starting from embeddings—vectors that map symbols to geometry—we show how an autoregressive decoder yields next-token predictions under causal masking. We contrast explicit Chain-of-Thought with implicit reasoning emerging in hidden states and attention. HRM introduces nested loops: a fast inner loop refining hypotheses and a slower outer loop coordinating multi-step inference—bringing System-1 speed and System-2 deliberation into one design. We discuss why compact, task-specialised HRMs can rival larger models, the trade-offs (e.g., per-task retraining), and possible extensions. 

• 11/07/2025 -- Academic Job Market Discussion
  Speakers: Rocío Díaz Martín (FSU), Ali Kara (FSU), Zhe Su (Auburn), Zezhong Zhang (Auburn)

• 11/14/2025
  Speaker: Mao Nishino

Title: The world of world models

Abstract: This review surveys recent developments in world models. In the broader pursuit of artificial general intelligence (AGI), a frequently cited missing piece between current large language models (LLMs) and AGI is a grounded understanding of the external world—a “world model.” Following the survey by Ding et al. and related work, I organize the literature into two strands: (1) representations of the world and (2) prediction of the future. For (1), I discuss model-based reinforcement learning techniques, such as Dreamer, alongside evidence for emergent world models in LLMs. For (2), I cover video-generation approaches (e.g., Sora and Genie) as well as research on embodied AI.

• 11/21/2025
  Speaker: Wenwen Li

Title: Persistent Model of the Second Configuration Space of Metric Star Graphs

Abstract:  In this talk, I will provide a brief introduction to the second configuration space of a metric graph X, denoted by X^2_{r,L}, with the restraint parameter r and edge length vector L = (L, L2, ..., Lk), where L2, ..., Lk are arbitrary but fixed positive real numbers. As the parameters r and L vary, these spaces form a natural bifiltration (denoted by X^2_{-,-}) that captures the evolution of topological features across two scales. In previous work, we showed that PH_i(X^2_{-,-}; F) is isomorphic to a tame 2-parameter persistence module N, i.e., the restriction of N to each chamber of the parameter space is a constant functor for all i >= 0.
Next, I will specialize to X = Star_k (the star graph with k edges) and present joint work with Murad Ozaydin on the 2-parameter persistence modules PH_i((Star_k)^2_{-,-}; F). In this project, we investigate the indecomposable direct summands of these 2-parameter persistence modules. We construct a bipartite weighted graph (G_k)L with fixed edge length vector L in (R{>0})^k and define filtering functions on its vertices and edges to obtain a natural filtration (G_k){-,L}. We show that the filtration (G_k){-,L} is compatible with L up to homotopy and therefore obtain a multifiltration (G_k){-,-} (in the homotopy category). We refer to (G_k){-,-} as the persistent bipartite model of (Star_k)^2_{-,-}. This construction yields an isomorphism between the associated (k+1)-parameter persistence modules PH_i((Star_k)^2_{-,-}; F) and PH_i((G_k)_{-,-}; F). By leveraging the persistent bipartite model with edge length vector L = (L, L2, ..., Lk), where L2, ..., Lk are arbitrary but fixed positive real numbers, we prove that the 2-parameter persistence module PH_1((Star_k)^2_{-,-}; F) is interval-decomposable for all k >= 3 (while PH_0((Star_k)^2_{-,-}; F) is not interval-decomposable for all k >= 3). Furthermore, our analysis provides an explicit description of all indecomposable direct summands of PH_1((Star_k)^2_{-,-}; F), up to isomorphism.