This Week in Mathematics


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Today:

Financial Mathematics Seminar [url]
Dynamic Risk Management Maximizing Growth and Value
- Gu Wang, WPI
Time: 3:05-3:55 Room: LOV 231
Abstract/Desc: This paper compares the risk management and payout policies of firms maximizing either assets’ average long-term growth or the present value of future dividends. When deleveraging incurs proportional costs, maximization of long-term growth entails managing leverage within a fixed range, depending on risk constraints and deleveraging costs, while avoiding bankruptcy at all times. Instead, maximization of dividends’ present value leads to a qualitatively different policy, with payouts when leverage is low and potential bankruptcy, as deleveraging is foregone altogether. Despite ostensible similarities, long-term growth and dividends’ present value entail substantively different objectives with distinct implications for risk.

Algebra seminar
Supersolvable posets and fiber-type arrangements
- Christin Bibby, Louisiana State University
Time: 3:05PM Room: 301
Abstract/Desc: We present a combinatorial analysis of fiber bundles of generalized configuration spaces on connected abelian Lie groups. These bundles are akin to those of Fadell--Neuwirth for configuration spaces, and their existence is detected by a combinatorial property of an associated finite partially ordered set. We obtain a combinatorially determined class of K(pi,1) spaces, and under a stronger combinatorial condition prove a factorization of the Poincar\'e polynomial when the Lie group is noncompact. In the case of toric arrangements, this provides an analogue of Falk--Randell's formula relating the Poincar\'e polynomial to the lower central series of the fundamental group. This is joint work with Emanuele Delucchi.

Entries for this week: 8

Monday November 18, 2024

Special Machine Learning Seminar
The Most (Subjectively) Interesting Bottlenecks of Large Language Models Development
- Ivan Yamshchikov, Center for Artificial Intelligence, Technical University of Applied Sciences Würzburg-Schweinfurt
Time: 3:05pm Room: LOV 105
Abstract/Desc: Since the release of ChatGPT Large Language Models (LLMs) are constantly mentioned whenever someone tries to speculate about potential impacts of machine learning. The size of these models makes it very hard to run reproducible experiments with them from scratch. However, LLMs are not omnipotent and there are several bottlenecks that could be vital for further progress in this field. What is particularly interesting is that one can experiment with those bottlenecks on a relatively low budget. In my talk I will try to highlight the areas of research that I personally find particularly interesting. We will start with some fundamentals of LLMs such as more efficient tokenisation procedures and then try to spread out into several application areas such as personalisation, for example, methods to assess how an LLM-based system can emulate empathetic behaviour and domain adaptation from ancient dead languages to highly specific scientific domains .

Analysis and PDE Seminar
Fractal Riesz Energy Asymptotics through Gaussian Means
- Jonathan Schillinger, FSU
Time: 3.05pm Room: LOV 231
Abstract/Desc: Studying the behavior of the minimal continuous Riesz energy over fractal sets has been a relatively hot topic in the field of Energy Theory. A recent result of Calef in 2010 computed the asymptotics for the minimal Riesz energy as the Riesz parameter s approaches the ambient dimension over self similar fractal sets. After introducing the problem and going through Calef's second order density arguments, we will discuss how a seemingly unrelated result for the Gaussian energy not only implies Calef's computation, but also extends to non-minimal cases.

Tuesday November 19, 2024

ACM
Learning Interaction Kernels from Mean-Field Models
- Weiqi Chu, Umass Amherst
Time: 3:05 pm Room: 0231
Abstract/Desc: Consider a complex system of a vast number of interacting agents, which can give rise to emergent collective behaviors such as bird flocking, fish swarming, and opinion formation — phenomena that cannot be obtained by studying individual agents alone. However, high-dimensional systems present significant challenges for inference tasks, particularly when data availability is limited. In this presentation, I will discuss how a mean-field approach can be used to derive mean-field models from agent-based dynamics and to infer interaction kernels with limited data observation. I will also address the PDE-constrained optimization method employed and highlight the identifiability challenges that commonly arise in such inference problems.

ATE
Optimality Properties of Tight Frames
- Ferhat Karabatman, FSU
Time: 1:00p Room: LOV 306
Abstract/Desc: Frames in Hilbert spaces are redundant sets that provide flexible and robust tools for signal representation and reconstruction. In this work, we explore the elegant mathematical properties of frames, with a particular focus on tight frames and their significance in communication systems. Tight frames are especially valued for their resilience to noise and efficient reconstruction properties. We present several key theorems that establish foundational results about tight frames in Hilbert spaces. Furthermore, we extend the concept of frames to tangent bundles over manifolds, providing a generalized framework for analyzing smooth vector bundles. In this extended setting, we prove that tight frames retain their robustness to noise, making them a valuable tool for manifold-based signal processing and geometric applications.

Wednesday November 20, 2024

Biomathematics Seminar
Sex Differences in Cell Metabolism
- Mike Reed (virtual), Duke University
Time: 3:05 Room: 232 Love
Abstract/Desc: Most of what we know about human physiology has been derived from clinical studies on men or experimental studies on male rats or mice. For a long time and for many different reasons, physiological research assumed that, except for obvious differences in the genitals, women are just like men. The clear behavioral differences (for example, women are more likely to be depressed than men) were thought to be explained by non-physiological causes better left to social scientists. Recent research shows that female physiology and male physiology are really different. During the years of menstruation, estrogen (and the androgens) effects many enzymes in cell metabolism. The differences are large and medically significant, showing that, in many cases, treatment and dosing should be different for men and women. This has opened up an exciting new field and, as always, mathematics is essential for the investigation and determination of underlying biological and medical mechanisms.

Biomath Journal Club [url]
Active licking shapes cortical taste coding
- Greg Owanga, FSU Mathematics
Time: 5:00 PM Room: Dirac 216

Thursday November 21, 2024

Financial Mathematics Seminar [url]
Dynamic Risk Management Maximizing Growth and Value
- Gu Wang, WPI
Time: 3:05-3:55 Room: LOV 231
Abstract/Desc: This paper compares the risk management and payout policies of firms maximizing either assets’ average long-term growth or the present value of future dividends. When deleveraging incurs proportional costs, maximization of long-term growth entails managing leverage within a fixed range, depending on risk constraints and deleveraging costs, while avoiding bankruptcy at all times. Instead, maximization of dividends’ present value leads to a qualitatively different policy, with payouts when leverage is low and potential bankruptcy, as deleveraging is foregone altogether. Despite ostensible similarities, long-term growth and dividends’ present value entail substantively different objectives with distinct implications for risk.

Algebra seminar
Supersolvable posets and fiber-type arrangements
- Christin Bibby, Louisiana State University
Time: 3:05PM Room: 301
Abstract/Desc: We present a combinatorial analysis of fiber bundles of generalized configuration spaces on connected abelian Lie groups. These bundles are akin to those of Fadell--Neuwirth for configuration spaces, and their existence is detected by a combinatorial property of an associated finite partially ordered set. We obtain a combinatorially determined class of K(pi,1) spaces, and under a stronger combinatorial condition prove a factorization of the Poincar\'e polynomial when the Lie group is noncompact. In the case of toric arrangements, this provides an analogue of Falk--Randell's formula relating the Poincar\'e polynomial to the lower central series of the fundamental group. This is joint work with Emanuele Delucchi.

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This Week in Mathematics