|
|
| (34 intermediate revisions by the same user not shown) |
| Line 1: |
Line 1: |
| | | | |
| − | '''Wednesdays at 4pm EDT'''<br /> | + | '''Mondays at 4pm EDT'''<br /> Armstrong Hall 315 |
| − | [https://wvu.zoom.us/j/96317244165?pwd=YVJGWHdxb2lGUHlkZEdRT1NPRFFsUT09 zoom link] (pass ''mathAdi2'') | + | [https://wvu.zoom.us/j/91064873237?pwd=R2lMSkpDUHREaU1xeUdDeVJHT2ZaUT09 zoom link] (pass ''euclid2022'') |
| | | | |
| | | | |
| − | The 2021-2022 Applied Mathematics Seminar is organized by Adrian Tudorascu and Casian Pantea. | + | The 2022-2023 WVU Math Colloquium is organized by Chris Ciesielski, Robert Mnatsakanov and Casian Pantea. |
| − | The talks are on zoom until further notice. The regular time for the Seminar is on Wednesday at 4:00 p.m. (in some cases we will schedule the seminar at different times, to accommodate speakers).
| + | Talks are usually held on Mondays at 4pm in Armstrong Hall 315 (in some cases we will schedule the seminar at different days/times, to accommodate speakers). |
| | | | |
| − | If you'd like to suggest speakers for the fall semester please contact Adrian or Casian. | + | If you'd like to suggest speakers for the fall semester please contact Chris, Robert, or Casian. |
| | | | |
| | | | |
| Line 19: |
Line 19: |
| | !align="left" | notes | | !align="left" | notes |
| | |- | | |- |
| − | |December 1 | + | |September 15 |
| − | | Veronica Ciocanel | + | | Dehua Wang |
| − | | Duke University | + | | University of Pittsburgh |
| − | |[[#Veronica Ciocanel | TBA ]] | + | |[[#Dehua Wang | Elastic effects on vortex sheets and vanishing viscosity ]] |
| | + | | 2:30pm, 315 ARM |
| | | | | | |
| | |- | | |- |
| − | |November 17 | + | |October 17 |
| − | | Radu Precup | + | | Farhad Jafari |
| − | | Babes-Bolyai University | + | | University of Minnesota |
| − | |[[#Radu Precup | Harnack type inequalities and localization of solutions ]] | + | |[[#Farhad Jafari | Variational Problems, Moment Sequences and Positive Definiteness ]] |
| | | | | | |
| | |- | | |- |
| − | |November 10 | + | |October 24 |
| − | | Jue Wang | + | | Tóth János |
| − | | Union College | + | | Budapest University of Technology and Economics |
| − | |[[#Jue Wang | Locating Objects of Interest from Screening Ultrasound ]] | + | |[[#Tóth János | The concept of reaction extent ]] |
| | | | | | |
| | |- | | |- |
| − | |November 3 | + | |October 31 |
| − | | Matthew Johnston | + | | Zi-Xia Song |
| − | | Lawrence Technological University | + | | University of Central Florida |
| − | |[[#Matthew Johnston | A Mathematical Model of COVID-19 Spread by Vaccination Status ]] | + | |[[#Zi-Xia Song | Coloring Graphs with Forbidden Minors ]] |
| | | | | | |
| | |- | | |- |
| − | |October 20 | + | |November 14 |
| − | | Xiang Xu | + | | Benjamin Bagozzi |
| − | | Old Dominion University | + | | University of Delaware |
| − | |[[#Xiang Xu | Blowup rate estimates of a singular potential in the Landau-de Gennes theory for liquid crystals ]]
| + | |[[#Benjamin Bagozzi | Understanding the Politics of Information Access in Big Data Contexts ]] |
| − | |
| |
| − | |-
| |
| − | |September 28
| |
| − | | Lorand Parajdi
| |
| − | | WVU
| |
| − | |[[#Lorand Parajdi | On the controllability of some systems modeling cell dynamics related to leukemia ]] | |
| − | |
| |
| − | |-
| |
| − | |September 15
| |
| − | | Adrian Tudorascu
| |
| − | | WVU
| |
| − | |[[#Adrian Tudorascu | On the convexity condition for the semi-geostrophic system ]]
| |
| − | |
| |
| − | |-
| |
| − | |September 28
| |
| − | | Lorand Parajdi
| |
| − | | WVU
| |
| − | |[[#Lorand Parajdi | On the controllability of some systems modeling cell dynamics related to leukemia ]]
| |
| − | |
| |
| | |} | | |} |
| | | | |
| | =Abstracts= | | =Abstracts= |
| | | | |
| − | ===Veronica Ciocanel=== | + | ===Dehua Wang=== |
| − | | |
| − | TBA
| |
| − | | |
| − | ===Radu Precup===
| |
| − | | |
| − | Harnack type inequalities and localization of solutions
| |
| − | | |
| − | First it is explained the problem of localization of solutions for boundary value problems in general. Next, the focus will be on radial solutions for phi-Laplace equations. Numerical solutions are obtained for some concrete equations.
| |
| − | | |
| − | ===Jue Wang===
| |
| − | | |
| − | Locating Objects of Interest from Screening Ultrasound
| |
| − | | |
| − | A fast Enclosure Transform is developed to localize complex objects of interest from medical ultrasound images. This approach explores spatial constraints on regional features from a sparse image feature representation. Unrelated, broken ridge features surrounding an object are organized collaboratively, giving rise to the enclosureness of the object. Three enclosure likelihood measures are constructed, consisting of the enclosure force, potential energy, and encloser count. In the transform domain, the local maxima manifest the locations of interest objects, for which only the intrinsic dimension is known a priori. I will demonstrate two medical applications in detecting (1) suspicious breast masses in screening breast ultrasound, and (2) the location of the prostate on trans-abdominal ultrasound for verification of patient positioning in radiotherapy treatment of prostate cancer.
| |
| − | | |
| − | ===Matthew Johnston===
| |
| − | | |
| − | A Mathematical Model of COVID-19 Spread by Vaccination Status
| |
| − | | |
| − | The novel coronavirus SARS-CoV-2, and the corresponding illness COVID-19, has afflicted hundreds of millions of people worldwide, killed at least 5 million, and devastated the world economy. The rapid development of effective and safe vaccines, which were authorized in the United States under Emergency Use Authorization in December 2020, have offered some hope that the end of the pandemic may be sight; however, at the same time we have seen the rise of variants, such as Delta, which are much more transmissible than the original strains. In this talk, I will introduce an n-stage vaccination model and corresponding system of differential equations which can simulate a disease outbreak by breaking the population down according to their vaccination status. This allows the mitigation effects of vaccination and accelerating effects of variants such as Delta to be uncoupled from one another, and offers valuable insight for the future course of the COVID-19 pandemic. I fit the model to 2021 data from the Virginia Department of Health.
| |
| − |
| |
| − | ===Xiang Xu===
| |
| − | | |
| − | Blowup rate estimates of a singular potential in the Landau-de Gennes theory for liquid crystals
| |
| − | | |
| − | The Landau-de Gennes theory is a type of continuum theory that describes nematic liquid crystal configurations in the framework of the Q-tensor order parameter. In the free energy, there is a singular bulk potential which is considered as a natural enforcement of a physical constraint on the eigenvalues of symmetric, traceless Q-tensors. In this talk we shall discuss some analytic properties related to this singular potential. More specifically, we provide precise estimates of both this singular potential and its gradient as the Q-tensor approaches its physical boundary.
| |
| − | | |
| − | ===Lorand Parajdi===
| |
| − | | |
| − | On the controllability of some systems modeling cell dynamics related to leukemia
| |
| − | | |
| − | In this talk, I will present two control problems for a model of cell dynamics related to leukemia. The first control problem is in connection with classical chemotherapy, which indicates that the evolution of the disease under treatment should follow a prescribed trajectory assuming that the drug works by increasing the cell death rates of both malignant and normal cells. In the second control problem, as for targeted therapies, the drug is assumed to work by decreasing the multiplication rate of leukemic cells only, and the control objective is that the disease state reaches a desired endpoint. The solvability of the two problems as well as their stability is proved by using a general method of analysis. Some numerical simulations are included to illustrate the theoretical results and prove their applicability. The results can possibly be used to design therapeutic scenarios such that an expected clinical evolution can be achieved.
| |
| − | | |
| − | ===Adrian Tudorascu===
| |
| − | | |
| − | On the convexity condition for the semi-geostrophic system
| |
| − | | |
| − | We show that conservative distributional solutions to the Semi-Geostrophic system in a rigid domain are in some well-defined sense critical points of a time-shifted energy functional involving measure-preserving rearrangements of the absolute density and momentum, which arise as one-parameter flow maps of continuously differentiable, compactly supported divergence free vector fields. We also show directly, with no recourse to Monge- Kantorovich theory, that the convexity requirement on the modified pressure potentials arises naturally if these critical points are local minimizers of said energy functional for any admissible vector field.
| |
| − |
| |
| − | | |
| − | ===Giuseppe Negro===
| |
| − | | |
| − | Stability of sharp Fourier restriction to spheres
| |
| − | | |
| − | In dimension $d\in\{3, 4, 5, 6, 7\}$, we establish that the constant functions maximize the weighted $L^2(S^{d-1}) - L^4(R^d)$ Fourier extension estimate on the sphere, provided that the weight function is sufficiently regular and small, in a proper and effective sense which we will make precise. One of the main tools is an integration by parts identity, which generalizes the so-called "magic identity" of Foschi for the unweighted inequality with $d=3$, which is exactly the classical Stein-Tomas estimate.
| |
| − | | |
| − | Joint work with E.Carneiro and D.Oliveira e Silva.
| |
| − | | |
| − | ===Rajula Srivastava===
| |
| − | | |
| − | Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups
| |
| − | | |
| − | We discuss $L^p\to L^q$ estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups, sharp up to endpoints. The proof shall be reduced to estimates for standard oscillatory integrals of Carleson-Sj\"olin-H\"ormander type, relying on the maximal possible number of nonvanishing curvatures for a cone in the fibers of the associated canonical relation. We shall also discuss a new counterexample which shows the sharpness of one of the edges in the region of boundedness. Based on joint work with Joris Roos and Andreas Seeger.
| |
| − | | |
| − | ===Itamar Oliveira===
| |
| − | | |
| − | A new approach to the Fourier extension problem for the paraboloid
| |
| − | | |
| − | An equivalent formulation of the Fourier Extension (F.E.) conjecture for a compact piece of the paraboloid states that the F.E. operator maps $ L^{2+\frac{2}{d}}([0,1]^{d}) $ to $L^{2+\frac{2}{d}+\varepsilon}(\mathbb{R}^{d+1}) $ for every $\varepsilon>0 $. It has been fully solved only for $ d=1 $ and there are many partial results in higher dimensions regarding the range of $ (p,q) $ for which $L^{p}([0,1]^{d}) $ is mapped to $ L^{q}(\mathbb{R}^{d+1}) $. One can reduce matters to proving that a model operator satisfies the same mapping properties, and we will show that the conjecture holds in higher dimensions for tensor functions, meaning for all $ g $ of the form $ g(x_{1},\ldots,x_{d})=g_{1}(x_{1})\cdot\ldots\cdot g_{d}(x_{d}) $. We will present this theorem as a proof of concept of a more general framework and set of techniques that can also address multilinear versions of this problem and get similar results. This is joint work with Camil Muscalu.
| |
| − | | |
| − | ===Changkeun Oh===
| |
| − | | |
| − | Decoupling inequalities for quadratic forms and beyond
| |
| − | | |
| − | In this talk, I will present some recent progress on decoupling inequalities for some translation- and dilation-invariant systems (TDI systems in short). In particular, I will emphasize decoupling inequalities for quadratic forms. If time permits, I will also discuss some interesting phenomenon related to Brascamp-Lieb inequalities that appears in the study of a cubic TDI system. Joint work with Shaoming Guo, Pavel Zorin-Kranich, and Ruixiang Zhang.
| |
| − | | |
| − | ===Alexandru Ionescu===
| |
| − | | |
| − | Polynomial averages and pointwise ergodic theorems on nilpotent groups
| |
| − | | |
| − | I will talk about some recent work on pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two. Our proof is based on almost-orthogonality techniques that go far beyond Fourier transform tools, which are not available in the non-commutative nilpotent setting. In particular we develop what we call a nilpotent circle method}, which allows us to adapt some the ideas of the classical circle method to the setting of nilpotent groups.
| |
| − | | |
| − | ===Liding Yao===
| |
| − | | |
| − | An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains
| |
| − | | |
| − | Given a bounded Lipschitz domain $\Omega\subset\mathbb{R}^n$, Rychkov showed that there is a linear extension operator $\mathcal E$ for $\Omega$ which is bounded in Besov and Triebel-Lizorkin spaces. We introduce a class of operators that generalize $\mathcal E$ which are more versatile for applications. We also derive some quantitative blow-up estimates of the extended function and all its derivatives in $\overline{\Omega}^c$ up to boundary. This is a joint work with Ziming Shi.
| |
| − | | |
| − | ===Lingxiao Zhang===
| |
| | | | |
| − | Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition
| + | '''''Elastic effects on vortex sheets and vanishing viscosity''''' |
| | | | |
| − | We study operators of the form
| + | Elasticity is important in continuum mechanics with a wide |
| − | $Tf(x)= \psi(x) \int f(\gamma_t(x))K(t)\,dt$
| + | range of applications and is challenging in analysis. In this talk we |
| − | where $\gamma_t(x)$ is a real analytic function of $(t,x)$ mapping from a neighborhood of $(0,0)$ in $\mathbb{R}^N \times \mathbb{R}^n$ into $\mathbb{R}^n$ satisfying $\gamma_0(x)\equiv x$, $\psi(x) \in C_c^\infty(\mathbb{R}^n)$, and $K(t)$ is a `multi-parameter singular kernel' with compact support in $\mathbb{R}^N$; for example when $K(t)$ is a product singular kernel. The celebrated work of Christ, Nagel, Stein, and Wainger studied such operators with smooth $\gamma_t(x)$, in the single-parameter case when $K(t)$ is a Calder\'on-Zygmund kernel. Street and Stein generalized their work to the multi-parameter case, and gave sufficient conditions for the $L^p$-boundedness of such operators. This paper shows that when $\gamma_t(x)$ is real analytic, the sufficient conditions of Street and Stein are also necessary for the $L^p$-boundedness of $T$, for all such kernels $K$.
| + | shall first review some basic mathematical results and then discuss |
| | + | some special elastic effects in fluid flows. The first elastic effect |
| | + | is the stabilizing effect of elasticity on the vortex sheets in |
| | + | compressible elastic flows. Some recent results on linear and |
| | + | nonlinear stability of compressible vortex sheets will be presented. |
| | + | The second effect is on the vanishing viscosity process of |
| | + | compressible viscoelastic flows in the half plane under the no-slip |
| | + | boundary condition. Our results show that the deformation tensor can |
| | + | prevent the formation of strong boundary layers. The talk is based on |
| | + | the recent joint works with several collaborators. |
| | | | |
| − | ===Kasso Okoudjou=== | + | ===Farhad Jafari=== |
| | | | |
| − | An exploration in analysis on fractals
| + | '''''Variational Problems, Moment Sequences and Positive Definiteness''''' |
| | | | |
| − | Analysis on fractal sets such as the Sierpinski gasket is based on the spectral analysis of a corresponding Laplace operator. In the first part of the talk, I will describe a class of fractals and the analytical tools that they support. In the second part of the talk, I will consider fractal analogs of topics from classical analysis, including the Heisenberg uncertainty principle, the spectral theory of Schrödinger operators, and the theory of orthogonal polynomials.
| + | Our ability to reformulate many problems in science and engineering in terms of variational (and control) problems continue to keep this area of mathematics current and of great interest. In this presentation we reformulate these problems as problems in measure theory and use moment methods to study them. Relating variational problems to moment methods has brought new interest in moment methods, moment completion problems and algebras of rational functions. This talk will connect these areas and (briefly) will show applications of moment methods to reconstruction problems in tomography. |
| | | | |
| − | ===Rahul Parhi=== | + | ===Tóth János=== |
| | | | |
| − | On BV Spaces, Splines, and Neural Networks
| + | '''''The concept of reaction extent''''' |
| | | | |
| − | Many problems in science and engineering can be phrased as the problem
| + | The concept of reaction extent or the progress of a reaction, advancement of the reaction, conversion, etc. was introduced around 100 years ago. |
| − | of reconstructing a function from a finite number of possibly noisy | + | Most of the literature provides a definition for the exceptional case of a single reaction step or gives an implicit definition that cannot be made explicit. |
| − | measurements. The reconstruction problem is inherently ill-posed when
| + | Starting from the standard definition we extend the classic definition of the reaction extent in explicit form for an arbitrary number of species |
| − | the allowable functions belong to an infinite set. Classical techniques | + | and of reaction steps and arbitrary kinetics. Then, we study the mathematical properties (evolution equation, continuity, monotony, differentiability, etc.) of the defined quantity, and connect them to the formalism of modern reaction kinetics. |
| − | to solve this problem assume, a priori, that the underlying function has
| + | Our approach tries to adhere to the customs of chemists and be mathematically correct simultaneously. |
| − | some kind of regularity, typically Sobolev, Besov, or BV regularity. The
| |
| − | field of applied harmonic analysis is interested in studying efficient
| |
| − | decompositions and representations for functions with certain
| |
| − | regularity. Common representation systems are based on splines and
| |
| − | wavelets. These are well understood mathematically and have been
| |
| − | successfully applied in a variety of signal processing and statistical
| |
| − | tasks. Neural networks are another type of representation system that is
| |
| − | useful in practice, but poorly understood mathematically.
| |
| | | | |
| − | In this talk, I will discuss my research which aims to rectify this
| + | We also show how to apply this concept to exotic reactions: reactions with more than one stationary state, oscillatory reactions, and reactions showing chaotic behavior. With the new definition, one can calculate not only the time evolution of the concentration of each reacting species but also the number of occurrences of the individual reaction events. |
| − | issue by understanding the regularity properties of neural networks in a
| |
| − | similar vein to classical methods based on splines and wavelets. In
| |
| − | particular, we will show that neural networks are optimal solutions to
| |
| − | variational problems over BV-type function spaces defined via the Radon
| |
| − | transform. These spaces are non-reflexive Banach spaces, generally
| |
| − | distinct from classical spaces studied in analysis. However, in the
| |
| − | univariate setting, neural networks reduce to splines and these function
| |
| − | spaces reduce to classical univariate BV spaces. If time permits, I will
| |
| − | also discuss approximation properties of these spaces, showing that they | |
| − | are, in some sense, "small" compared to classical multivariate spaces
| |
| − | such as Sobolev or Besov spaces.
| |
| | | | |
| − | This is joint work with Robert Nowak. | + | This is joint work with Vilmos Gáspár. |
| | | | |
| − | =[[Previous_Analysis_seminars]]= | + | === Zi-Xia Song=== |
| | | | |
| − | https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars
| + | '''''Coloring Graphs with Forbidden Minors''''' |
| | | | |
| − | =Extras=
| + | [[Media:SongAbstract.png|'''Abstract link''']] |
| | | | |
| − | [[Blank Analysis Seminar Template]]
| |
| | | | |
| | + | ===Benjamin Bagozzi=== |
| | | | |
| − | Graduate Student Seminar:
| + | '''''Understanding the Politics of Information Access in Big Data Contexts''''' |
| | | | |
| − | https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html
| + | Access to information (ATI) systems empower groups and individuals to request information from their governments and obligate these governments to respond, subject to certain legal exemptions. These systems are now in operation in over 100 countries worldwide. The data that are generated by ATI systems can often be characterized as having (i) fine-grained spatio-temporal properties, (ii) extensive amounts of text, (iii) sender-receiver characteristics, and (iv) potential privacy concerns. For political science, such data offer researchers an opportunity to study questions related to government responsiveness, bureaucratic performance, and public accountability at near-unprecedented levels of disaggregation. This presentation highlights the opportunities and challenges associated with ATI data for both data science and political science audiences. Its focus is primarily on Mexico's federal ATI system and over two million associated ATI requests and responses covering the 2003-2020 period. Applications of supervised and unsupervised machine learning tools to the texts of these requests and their responses will be presented, alongside analyses of these request-response measures in relation to government responsiveness in Mexico. |
Mondays at 4pm EDT
Armstrong Hall 315
zoom link (pass euclid2022)
The 2022-2023 WVU Math Colloquium is organized by Chris Ciesielski, Robert Mnatsakanov and Casian Pantea.
Talks are usually held on Mondays at 4pm in Armstrong Hall 315 (in some cases we will schedule the seminar at different days/times, to accommodate speakers).
If you'd like to suggest speakers for the fall semester please contact Chris, Robert, or Casian.
Schedule
Abstracts
Dehua Wang
Elastic effects on vortex sheets and vanishing viscosity
Elasticity is important in continuum mechanics with a wide
range of applications and is challenging in analysis. In this talk we
shall first review some basic mathematical results and then discuss
some special elastic effects in fluid flows. The first elastic effect
is the stabilizing effect of elasticity on the vortex sheets in
compressible elastic flows. Some recent results on linear and
nonlinear stability of compressible vortex sheets will be presented.
The second effect is on the vanishing viscosity process of
compressible viscoelastic flows in the half plane under the no-slip
boundary condition. Our results show that the deformation tensor can
prevent the formation of strong boundary layers. The talk is based on
the recent joint works with several collaborators.
Farhad Jafari
Variational Problems, Moment Sequences and Positive Definiteness
Our ability to reformulate many problems in science and engineering in terms of variational (and control) problems continue to keep this area of mathematics current and of great interest. In this presentation we reformulate these problems as problems in measure theory and use moment methods to study them. Relating variational problems to moment methods has brought new interest in moment methods, moment completion problems and algebras of rational functions. This talk will connect these areas and (briefly) will show applications of moment methods to reconstruction problems in tomography.
Tóth János
The concept of reaction extent
The concept of reaction extent or the progress of a reaction, advancement of the reaction, conversion, etc. was introduced around 100 years ago.
Most of the literature provides a definition for the exceptional case of a single reaction step or gives an implicit definition that cannot be made explicit.
Starting from the standard definition we extend the classic definition of the reaction extent in explicit form for an arbitrary number of species
and of reaction steps and arbitrary kinetics. Then, we study the mathematical properties (evolution equation, continuity, monotony, differentiability, etc.) of the defined quantity, and connect them to the formalism of modern reaction kinetics.
Our approach tries to adhere to the customs of chemists and be mathematically correct simultaneously.
We also show how to apply this concept to exotic reactions: reactions with more than one stationary state, oscillatory reactions, and reactions showing chaotic behavior. With the new definition, one can calculate not only the time evolution of the concentration of each reacting species but also the number of occurrences of the individual reaction events.
This is joint work with Vilmos Gáspár.
Zi-Xia Song
Coloring Graphs with Forbidden Minors
Abstract link
Benjamin Bagozzi
Understanding the Politics of Information Access in Big Data Contexts
Access to information (ATI) systems empower groups and individuals to request information from their governments and obligate these governments to respond, subject to certain legal exemptions. These systems are now in operation in over 100 countries worldwide. The data that are generated by ATI systems can often be characterized as having (i) fine-grained spatio-temporal properties, (ii) extensive amounts of text, (iii) sender-receiver characteristics, and (iv) potential privacy concerns. For political science, such data offer researchers an opportunity to study questions related to government responsiveness, bureaucratic performance, and public accountability at near-unprecedented levels of disaggregation. This presentation highlights the opportunities and challenges associated with ATI data for both data science and political science audiences. Its focus is primarily on Mexico's federal ATI system and over two million associated ATI requests and responses covering the 2003-2020 period. Applications of supervised and unsupervised machine learning tools to the texts of these requests and their responses will be presented, alongside analyses of these request-response measures in relation to government responsiveness in Mexico.
