Colloquia
Department of Mathematics and Statistics
Texas Tech University
We review developments on generalized Fréchet functionals aiming at describing the possible influence of dependence on functionals of a statistical experiment, where the marginal distributions are fixed. The problem of mass transportation between two masses (distributions) can be seen as a particular case of this problem with two marginals and a linear functional induced by a distance. We also describe several results for the solution for nonlinear functionals in the context of the analysis of worst case risk distributions. We show that these problems can be reduced to a variational problem and the solution of a finite
class of (linear) mass transportation problems.
In the third part of the talk we review several recent methods to improve bounds for aggregated portfolios of risks by including additional to the marginal information some structural and partial dependence information. Several applications show that these improved risk bounds may lead to results acceptable in praxis.
Please attend this Dr. Rüschendorf's colloquium on Thursday, January 14th at 1 PM CST via this Zoom link, passcode 692674.
Linear algebra deals with discrete vectors and matrices, and MATLAB was built on giving easy access to these structures and the best algorithms for working with them. But almost everything in linear algebra has a continuous analogue, where vectors become functions and matrices become operators. The Chebfun project develops this analogy with mathematics, algorithms, and software, and the talk will present ideas and Chebfun demonstrations in areas including matrix factorizations, complex variables, differential equations, and data science. Once you start thinking and computing this way, it's hard to go back.Presently, it is well understood what geometric features are necessary and sufficient to guarantee the boundedness of convolution-type singular integral operators (SIO's) on Lebesgue spaces. This being said, dealing with other function spaces where membership entails more than a mere size condition (like Sobolev spaces, Hardy spaces, or the John-Nirenberg space BMO) requires new techniques. In this talk I will explore recent progress in this regard, and follow up the implications
of such advances into the realm of boundary value problems.
We will embark on a ~20-years through time journey in the Quant Risk Space - what has happened and what is to be expected across Academic Research, Practitioners Need and Data:
• The impact of 2008
• Advances in the Market&Credit Risk Models
• The “small data segment” - Private Equity & Real Estate
• What does big data contribute to the Quant& Risk Space
• The future – Climate Risk, ESG and beyond
Wikipedia: Environmental, Social, and Corporate Governance (ESG) refers to the three central factors in measuring the sustainability and societal impact of an investment in a company or business.Many biological organisms are comprised of deformable porous media, with additional complexity of an embedded muscle. Using geometric variational methods, we derive the equations of motion of a for the dynamics of such an active porous media. The use of variational methods allows to incorporate both the muscle action and incompressibility of the fluid and the elastic matrix in a consistent, rigorous framework, with no need to guess the balance of forces. We then derive conservation laws for the motion, perform numerical simulations and show the possibility of self-propulsion of a biological organism due to particular running wave-like application of the muscle stress.The first part of the talk will review robust regression and especially an optimal bias robust regression method. The second part of the talk is empirical and applied, and will show that the Fama-French 1992 result is very biased due to outliers, and the robust regression gives opposite conclusions with regard to the size factor and the beta factor. We obtain similar conclusions and other interesting results for the 1980 - 2018 time period. Zoom meeting at 3 PM CST via this zoom link, passcode 751413
This Colloquium is presented in conjuction with the Mathematical Finance seminar group.Modeling the behavior of speculative assets has long been a challenge both from a theoretical and from an empirical viewpoint. Traditionally, financial economists have resorted to readily available results and tools from mathematics and statistics. In doing so, mismatches between the assumptions underlying these tools and relevant empirical facts governing financial markets have commonly been ignored. In this talk, we look at some of these mismatches, their consequences and possible solutions. Specifically, we look at questions concerning risk assessment, temporal and cross-sectional dependence structures, and also take a look at the rise of crypto currencies.
Dr. Mittnik's talk is given in conjunction with the Mathematical Finance seminar group, and is held in honor of Dr. Bijoy Ghosh's 65th birthday!In this talk I will discuss a version of the Divergence Theorem for vector fields which may lack any type of continuity and for which the boundary trace is taken in a strong, nontangential pointwise sense. These features of our brand of Divergence Theorem make it an effective tool in dealing with problems arising in various areas of mathematics,including Harmonic Analysis, Complex Analysis, Potential Analysis, and Partial Differential Equations. A few such applications will be discussed.
Please virtually attend Dr. Mitrea's colloquium via this zoom link on Thursday the 4th at 3:30 PM.Roundtable panel discussion with senior industry “quants” on the subject: “What it takes to be a Quant?”
Please attend Dr. Carr's colloquium at 2 PM, Friday the 5th, via this Zoom link.
Zoom Meeting ID: 998 6719 2059 Passcode: 309286The Covid-19 pandemic has been a major public health and economic challenge worldwide. Mathematical models are powerful tools for forecasting epidemiological infection evolution and the necessary social interventions and their effects. Here, we present a compartment model that mechanistically takes into account Covid-19 features that are not captured by traditional models. By simple idealization we have developed a dynamical system model consisting of eight coupled ordinary differential equations representing susceptible (S), sequestered (Q), undetected infected (U), detected infected (I), detected dead (D), undetected recovered (E), and detected recovered populations (R) – the SQUIDER model. Applied to all US states, particularly eight most populous states, 49 countries of Europe, and also six states in South Asia, our model adequately predicts major metrics, such as Covid-19 infection and death rates, as well as predictions of the end of the pandemic. Also addressed are the impact of mobility interventions such as shelter-at-home practices via percentage of the population sequestered, as well as other non-pharmaceutical health interventions such as mask wearing, at different time points in the pandemic evolution.
This Colloquium is held in conjunction with the Applied Math seminar group, and is a collaborative work with Dr.'s Fazle Hussain and Frank Van BusselReconnection is the process by which two approaching vortices cut and connect to each other. As a topological change event, it has been a subject of considerable fundamental interest for decades – not only in (classical) viscous and quantum fluids but also in many other fields, such as plasmas, polymers, DNAs, and macromolecules. For viscous fluid flows, reconnection is believed to play a significant role in various phenomena, such as turbulence cascade, fine-scale mixing, and aerodynamic noise generation. We first delineate the fundamental processes involved in vortex reconnection and its apparent role in turbulence cascade – a feature of turbulent flows that has eluded even the topmost brains. Vortex reconnection is also a fruitful avenue for understanding the long-standing and highly debated mathematical question regarding the occurrence of finite-time singularity of Navier-Stokes and Euler equations. We also show that reconnection is one of the main mechanisms for aeroacoustic noise generation. In addition, we address the helicity dynamics related to reconnection, including core dynamics, polarized vortex reconnection, and helicity conservation among different forms, e.g., link, writhe, and twist. Finally, the similarity between classical (viscous) and quantum reconnections are discussed.
This work is done with Dr. Jie Yao, TTU Mechanical Engineering PostDoc Researcher
Presented jointly with the Applied Math seminar group, watch this Colloquium at 3 PM CST via this zoom link.When considering the semi-discrete and fully discrete versions of the original "smooth" mKdV equation, particular choices must be made, and justifications for those choices are needed in order to believe the discretizations are correct. What makes a discretization "correct" is that it has a rich mathematical structure, often imitating, and sometimes expanding upon, the structure found in the original smooth equation. In the case at hand, such justifications have been established (by Inoguchi, Kaji, Kajiwara, Ohta, Matsuura, Park and others), and here we (joint work with Joseph Cho and Tomoya Seno) add another structural layer by connecting discretized mKdV equations with the transformation theory of curves in the plane. We will see how transformation theory of surfaces in 3-space has provided elegant approaches for discretizing surfaces, and curves as well, giving us a backdrop for describing the tools we need -- isoperimetric flows, and both discrete and infinitesimal Darboux transformations, of planar curves. The permutability characteristics of these transformations provide a computationally quick avenue to the discretized mKdV equations, bringing more geometry into the underlying mathematical structure, and additionally showing these discretizations are compatible with transformation theory of geometric objects.
There is a categorically new way to fight disease, which could have a significant impact on the COVID pandemic now. Its origins come from math, game theory, and computer science. It works against every COVID variant, and would play a key role in mopping up vaccine-resistant infections to block COVID's evolution. It's an app which is fundamentally different from every other app (and which resolves deep flaws in "contact tracing apps").
Functionally, it gives you an anonymous radar that tells you how "far" away COVID has just struck. "Far" is measured by counting physical relationships (https://novid.org, https://youtu.be/EIU-6FvwikQ).
The simple idea flips the incentives. Previous approaches were about controlling you, preemptively removing you from society if you were suspected of being infected. This new tool lets you see incoming disease to defend yourself just in time. This uniquely aligns incentives so that even if everyone in a democratic society does what is best for themselves, they end up doing what is best for the whole.
Please virtually attend today's Colloquium at 3 PM CDT via this zoom link
We will give an overview of how physics and homological algebra have met in the setting of gauge theory, with an emphasis on how the new subject of derived geometry provides a clarifying framework. The talk's concrete aim is to explain the Higgs mechanism as a case study. Our approach will be low-tech and will emphasize the motivations; anyone familiar with notions like vector bundle and cochain complex should be able to follow.
This Colloquium is held in conjunction with the Current Advances in Mathematics seminar group, and is a collaborative work with Dr. Chris Elliott.
Please virtually attend Dr. Gwilliam's Colloquium at 4 PM CDT (UTC-5) via this zoom linkWhat is the shape of a knot tied tight in rope? The ropelength problem asks us to minimize the length of a knot or link in space, subject to a thickness constraint that keeps a unit tube around the curve embedded. We derive a Balance Criterion giving necessary and sufficient conditions for a space curve to be ropelength-critical. Our approach is modeled on rigidity theory for frameworks and uses a new infinite-dimensional version of the Kuhn-Tucker theorem.
In terms of the core curve, the thickness constraint has two parts: an upper bound on curvature and a self-contact condition. The curvature bound is especially difficult to handle, as the curve may fail to be twice differentiable. In the end, we express thickness as the minimum of a compact family of smooth functions in order to apply Clarke's theorem on the derivative of such a minimum.
Using our balance criterion, we can give explicit descriptions of several tight links. The tight configuration of the Borromean rings, for instance, is piecewise smooth with 42 pieces. Even two simply clasped ropes surprising geometric behavior: there is a slight gap between them when they are pulled tight.
Finally, we will consider analogous problems for triply periodic knots and links, and for knot diagrams in the plane.
Please virtually attend Dr. Sullivan's colloquium via this zoom link on Wednesday the 31st at 2:00 PM, CDT (UTC-5).We will discuss a variational problem with parameters whose minimizers are isometric immersions of a given Riemannian surface in 3-space. One of the parameters controls the Willmore energy, which can be used as a regularizer preventing excessive creasing/crumpling of the resulting isometric immersion in 3-space.
Many continuous time stochastic systems that are modeled by SDE and SPDE have been limited to noise processes being Brownian motions. Brownian motion models have a well developed stochastic calculus and limiting behaviors that reflect the martingale, Markov and Gaussian properties of Brownian motion. However for many physical systems the empirical data do not justify the use of Brownian motion as the model for random disturbances. In fact Brownian motions provide models that are often far from the physical data. Thus it is necessary to find more general noise models and tractable methods to solve the associated problems of control or adaptive control. These other noise models include more general Gaussian processes and non-Gaussian processes. The talk focuses on new developments and new challenges in noise models for stochastic control and adaptive control problems.
Dr. Pasik-Duncan's colloquium is held in conjunction with the Applied Math seminar group. Virtually attend this colloquium at 4 PM CST (UTC -5) via this zoom link. The literature on the optimal harvest of fisheries has concentrated on a single fishing area with biomass uncertainty and to a lesser degree also with price uncertainty. We develop and implement a stochastic optimal control approach to determine the harvest that maximizes the value of a fishery participating in a global market, where all the considered harvesting zones sell their production. This market is characterized by an
inverse demand function, which combines an exogenous demand shock and the aggregate harvesting of all zones. Accordingly, a fishery's harvest will be affected by the global demand shocks and the harvesting in all the competing zones through the global selling price. In addition, we decompose the biomass uncertainty into local and global biomass shocks. Through global biomass shocks, the model provides enough flexibility
to acknowledge for correlation in the biomass shocks faced by the multiple perhaps adjacent areas. When we compare our global framework with an alternative where the individual
zones are aggregated into a single optimizing fishery we find that competition will increase the global harvest and consequently reduced the resource price.
This Colloquium is co-hosted with the Mathematical Finance seminar group. Join us at 4 PM CST (UTC-5) via this zoom link, passcode 886878The Departmental Scholarship and Awards Banquet will be held virtually, Friday, April 23rd at 3:30 PM This talk will be about various connections between the theory of transformation groups and commutative algebra, in particular, the homological properties of polynomial rings and of complete intersections rings. These concern numerical invariants associated with finite free complexes over such rings; notably, the length of the complex, the ranks of the free modules that appear in it, and the length of their homology modules. On the topological side, there are long-standing conjectures due to Adem, Browder, Carlsson, Halperin, and Swan, among others, about these invariants. Their commutative algebra counterparts are conjectures of Buchsbaum and Eisenbud, and Horrocks. My plan is to explain some of these connections, and recent developments that have spurred a resurgence of interest in them.
This Colloquium is held in conjunction with the Current Advances in Mathematics seminar group.