Colloquia
Department of Mathematics and Statistics
Texas Tech University
In this talk, we will discuss 4-dimensional complete (not necessarily compact) gradient shrinking Ricci solitons. We will show that a 4-dimensional complete gradient shrinking Ricci soliton satisfying a pointwise condition involving either the self-dual or anti-self-dual part of the Weyl tensor is either Einstein, or a finite quotient of either the Gaussian shrinking soliton $R^4,$ or $S^3\times R$, or $S^2\times R^2.$ In addition, we will present some new curvature estimates for 4-dimensional complete gradient Ricci solitons. Some open problems on this subject will also be discussed. This is joint work with Huai-Dong Cao and Detang Zhou.
This Colloquium is sponsored by the PDGMP seminar group, and may be attended virtually at this Zoom link Tuesday, March 1st at 3 PM (UT-6).
On finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class L+2 of bounded operators on separable infinite dimensional Hilbert spaces which can be written as the product of two bounded positive operators is studied. The structure is much richer, and connects (but is not equivalent to) quasi-similarity and quasi-affinity to a positive operator. The spectral properties of operators in L+2 are developed, and membership in L+2 among special classes, including algebraic and compact operators, is examined.
This Colloquium is sponsored by the Applied Math seminar group and may be attended virtually via this Zoom link this Thursday the 3rd at 3:30 PM (UT -6).
Details of Dr. Szmigielski's talk can be found at this pdf.
A classical problem going back to ancient Greece is to find the shortest curve in the plane enclosing a given area: the isoperimetric problem. A similar question is whether given a curve on a surface it can be deformed to the shortest one. Whilst the solutions to these classical problems are well-known, natural generalizations in higher dimensions are mostly unsolved. I will explain how this leads us to the study of minimal Lagrangians and the question of how to find them, which will take us to the interface between symplectic topology, Riemannian geometry, and analysis of nonlinear PDEs, with links to theoretical physics.
Please virtually attend Dr. Lotay's Colloquium at 3 PM (UT-5) this Thursday afternoon the 23rd, via this Zoom link.
The critical points of W-functional are shrinking gradient Ricci solitons (SGRS). It is well known that gradient Ricci solitons, which appeared in Ricci flows, are generalizations of Einstein manifolds and basic models for smooth metric measure spaces. One of the challenging problems is to classify all gradient Ricci solitons with constant scalar curvature. In joint work with X. Cheng, we prove that a 4-dimensional shrinking gradient Ricci soliton has constant scalar curvature if and only if it is either Einstein or a finite quotient of Gaussian shrinking soliton $\mathbb{R}^4$, $\mathbb{S}^2×\mathbb{R}^2 $ or $\mathbb{S}^3×\mathbb{R}$.
Please virtually attend Dr. Zhou's Colloquium at 3:30 PM (UT-5) this Thursday afternoon the 31st via this Zoom link.
Colloquium pdf
This Departmental SIAM Colloquium may be attended Tuesday the 5th at 3:15 PM CDT (UT-5) via this Zoom link.
Meeting ID: 955 5381 8766
Passcode: SIAM
One criticism of the classical Black-Scholes-Merton option pricing formulation is its use of a Gaussian price process for the asset underlying the option. As a result, various observed (“stylized”) facts of financial price processes remain uncaptured by the BSM model. These behaviors, which are observed in the return process (fractional change in price over time) and in the distribution of those returns over time, include volatility clustering, skewness and heavy tails. Going beyond a Gaussian model presents challenges, for example existing formalisms for option pricing cannot accommodate distributions with power-law tails such as Student’s t. In this talk I discuss the use of double subordinated Levy processes within established option pricing formalisms. In particular, inverse Gauss processes (https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution) are used to capture five stylized behaviors: the mean, volatility, skewness and kurtosis of the distribution of asset returns, as well as to capture the fact that information driving asset prices arrives at discrete, random intervals. This work will be presented in the context of European call and put options whose underlying asset is a portfolio. The specific portfolio consists of holdings in real estate investment trusts (REITs). A by-product of the use of subordinated methods is the natural definition of a new measure for the volatility of asset returns.
Colloquium flyer
Even if the ongoing digital transformation of industry and society presents great possibilities when it comes to efficiency, performance and adaptation, it exposes systems to new risks and vulnerabilities. Security and privacy is of growing concern in many control applications. Cyber-attacks are frequently reported for a variety of industrial and infrastructure systems. For more than a decade the control community has developed techniques for how to design control systems resilient to cyber-physical attacks. In this talk, we will review some of these results. In particular, as cyber and physical components of networked control systems are tightly interconnected, it is argued that traditional IT security focusing only on the cyber part does not provide appropriate solutions. Modeling the objectives and resources of the adversary together with the plant and control dynamics is shown to be essential. The consequences of common attack scenarios, such as denial-of-service, replay, and bias injection attacks, can be analyzed using the proposed framework. It is also shown how to strengthen the control loops by deriving security- and privacy-aware estimation and control schemes. Applications in building automation, power networks, and automotive systems will be used to motivate and illustrate the results. The presentation is based on joint work with several students and colleagues at KTH and elsewhere.
Colloquium flyer
While the long-term benefits of introducing connected and automated vehicles into road traffic are widely understood to be revolutionary, there is much debate about whether its early stages will cause an increase in congestion and issues related to human-driven vehicles. Notwithstanding, connected vehicles acting as mobile sensors and actuators could enable traffic predictions and control at a scale never before possible, and thereby a much more efficient use of the available road infrastructure. In this talk, we will present how a new freight transport technology based on automated truck platoons can be the backbone for such a system. Some basic theoretical and experimental results on the control and coordination of truck platoons will be presented. How such platoons influence traffic flows by acting as a moving bottleneck will be discussed together with traffic models suitable for designing novel traffic control systems. It will also be argued that these models are possible to learn automatically from data gathered by platoons acting as traffic flow sensors. Experiments show that relatively few connected vehicles are enough to mitigate stop-and-go waves and improve traffic conditions significantly. The presentation is based on joint work with Matthieu Barreau, Mladen Cicic, and others.
The annual spring Departmental Awards Ceremony honoring student scholarship, Departmental Excellence, and SIAM award recipients is a hybrid event and can be seen in Math 011 or attended Wednesday the 27th at 4:00 PM CDT (UT-5) via this Zoom link. Meeting ID: 964 5740 5000 no passcode
Following the online ceremony, an in-person joint Reception, graciously sponsored by Dr. Ghosh, for acclaimed Dayawansa Memorial Speaker Professor Karl Henrik Johansson and Honors Ceremony recipients will be held at 4:45 PM in the 1st Floor Lobby of the Math Buidling.
Colloquium flyer
Traditional control methods, such as model predictive control, are able to efficiently incorporate state and input constraints into the control synthesis problem. In this talk, we will discuss how more complex specifications based on linear temporal logic (LTL) can be included. We introduce the new notion of a temporal logic trees (TLT) and show how they can be derived from any LTL formula using classical reachability analysis. Conditions are given to verify whether a system satisfies an LTL formula by using TLT. The presented framework allows the treatment of uncertain and time-varying systems as well as environment models, different from many other approaches. We give an online control synthesis algorithm, under which a set of feasible control inputs can be generated at each time step and show that this algorithm is recursively feasible. The proposed method is demonstrated in applications of automated vehicles and shared-autonomy systems. The talk is mainly based on joint work with Yulong Gao, Frank Jiang, Mirco Giacobbe, and Alessandro Abate.
I will consider sequences of constant mean curvature (cmc) immersions $f_n $ of tori into $\mathbb R ^ 3 $ and explain under what circumstances a "blow up" (i.e. a rescaling of both the parameter for $f_n $ and that of the ambient Euclidean space) produces a sub-sequence whose limit is a minimal surface immersion. These surfaces are studied via the sinh-Gordon and KdV integrable systems respectively. In particular, certain optimally fast blow ups of cmc tori yield helicoids.
This is joint work with Sebastian Klein and Martin Schmidt (University of Mannheim).
This Departmental Colloquium may be attended Tuesday the 3rd at 3:30 PM CDT (UT-5) via this Zoom link.
Meeting ID: 953 6828 6693
Passcode: Carberry