October 20, 2023
Speaker: Brian Zilli
Title of the talk: Limit sets of computable sequences: definitions & summary of results
Abstract: We define computability of a sequence of reals and a way of measuring the computational complexity of closed sets of reals. We do this toward answering the problem: How computationally complex is the set of limit points of a computable sequence of reals? We prove only one short lemma giving an upper bound on complexity in preparation for a later talk where we will show the bound is saturated and other results (that will be stated without proof today).
October 13, 2023
Speaker: Mitchell Ashburn
Title of the talk: Lie groups and sub-Riemannian geodesics
Abstract: A Lie group is a group that is also a manifold, this gives it a bit more structure than an arbitrary manifold. We will utilize this additional structure to consider a sub-Riemannian problem SL(2). We call a metric sub-Riemannian if it is positive definite only on a subspace of the tangent bundle, this leads to the notion of a sub-Riemannian geodesic. This talk will start with an introduction to Lie groups followed by a summary of a part of the paper "Sub-Riemannian Geodesics on SL(2,R)" by Domenico D'Alessandro and Gunhee Cho.
October 6, 2023
Speaker: Mitch Haeuser
Title of the talk: Nonlocal equations on the boundary
Abstract: We will discuss regularity for a problem involving a fractional Dirichlet-to-Neumann operator associated to harmonic functions. In particular, we will define a fractional powers of the normal derivative, compatible Sobolev spaces, and consider various examples. We will further look at the extension problem characterization to obtain various estimates. This is joint work with Luis Caffarelli (UT Austin) and Pablo Raúl Stinga (Iowa State University)
September 22, 2023
Speaker: Chad Berner
Title of the talk: A Fourier expansion for singular measures on the real line and Fourier dextroduals
Abstract: We will discuss a Fourier expansion result for L^{2}(mu,R) where mu is a singular Borel probability measure on the real line using theory from the Kaczmarz algorithm. We also discuss examples, non-examples, and properties of measures on the torus that are not absolutely continuous or singular that admit Fourier frame-like expansions.
September 15, 2023
Speaker: Agil Muradov
Title of the talk: An alternate way for constructing the reals
Abstract: I will present an alternative way of constructing the set of real numbers, different from the Dedekind cuts and from the Eudoxus reals. Effectively I will be constructing the set of real numbers from just two integer numbers {0,1} but skipping explicitly constructing N, Z and Q.
September 8, 2023
Speaker: Billy Duckworth
Title of the talk: Eudoxus Reals
Abstract: I will present an unusual construction of the real numbers that goes by the name ‘Eudoxus Reals’. Its most striking feature is that it constructs the reals from the integers, skipping the rationals altogether.
January 27, 2022
Organizational Meeting.
March 31, 2023
Speaker : Mitchell Haeuser
Title of Talk : Nonlocal Equations on the Boundary
Abstract : We will discuss regularity for a problem involving a fractional Neumann boundary condition with harmonic interior. In particular, we will define a fractional normal derivative, compatible Sobolev spaces, and consider various examples. We will further look at the extension problem to obtain various estimates.
April 21, 2023
Speaker : Billy Duckworth
Title of Talk : All Topologies Come from Generalized Metrics (by Ralph Kopperman) s
Abstract : Most of us started our education in topology by first studying metric spaces. We quickly learn that there are many interesting and useful topological spaces that cannot have come from a metric. Various generalizations of the concept of metrics (such as are psuedo-metrics, quasi-metrics, etc...) are used in various areas, but none of them are general enough to describe arbitrary spaces. This paper discuses a way to generalize the concept of a metric in a broad enough way to make all topological spaces "metric" spaces. Further, some basic separation properties are described in terms of additional properties of this new distance function.
September 2, 2022
Organizational Meeting.
September 9, 2022
Speaker : Chad Berner
Title: Fourier Analysis from Singular Measures
Abstract: Any square integrable function on the torus is a norm limit of its Fourier series, but what if you change the measure from Lebesgue measure to a singular measure? It turns out you will lose orthogonality of the exponentials, but by the Kaczmarz algorithm, any function that is square integrable in this new measure space has a Fourier series converging in norm. We discuss further results in higher dimensions as well as analytic operators and their relation to the Hardy space and Fourier series.
September 16, 2022
Speaker: Brian Zilli
Title: Boundary Spectra of Uniform Frostman Blaschke Products
Abstract: In a 2006 paper, Alec Matheson proved that uniform Frostman Blaschke products have nowhere dense spectra and—conversely—that any closed, nowhere dense subset of the circle is the spectrum of some uniform Frostman Blaschke product. In this talk, we define these terms and outline the proof of Matheson’s first result.
September 23, 2022
Speaker: Mitch Haeuser
Title: Nonlocal equations on the boundary
Abstract: We will discuss regularity for a problem involving a fractional Dirichlet-to-Neumann operator associated to harmonic functions. In particular, we will define a fractional power of the normal derivative, compatible Sobolev spaces, and consider various examples. We will further look at the extension problem characterization to obtain various estimates. This is joint work with Luis Caffarelli (UT Austin) and Pablo Raúl Stinga (Iowa State University)
September 30, 2022
No Meeting.
October 7, 2022
Speaker: Joe Miller
Title: Multiplication Operators on Weighted Banach Spaces
Abstract: In 2016, Dr. Robert Allen and one of his students, Isaac Craig, studied multiplication operators on weighted Banach spaces of infinite trees. They characterized the bounded and compact multiplication operators in such a context and determined which were isometries. In this talk, we will define all these terms and understand these characterizations.
October 14, 2022
Speaker: Sarah McCarty
Title: Piecewise Linear Functions Representable with Infinite-Width Neural Networks
Abstract: A shallow neural network can be identified by the integral of the ReLU function with respect to a signed, finite measure on an appropriate parameter space. We map these measures on the parameter space with measures on the projective n-sphere cross R, allowing points in the parameter space to be bijectively mapped to hyperplanes in the domain of the function. This can in turn be mapped almost bijectively onto R^{n+1}. With these mappings and a large non-co-hyperplanar set, we can show that every continuous piecewise linear function expressible with an infinite width neural network is in fact expressible with a finite width network.
October 21, 2022
Speaker: Lillian Uhl (Rescheduled for October 28)
October 28, 2022
Speaker: Lillian Uhl
Title: Categorical Aspects of Integration Theory and Operator Algebras
Abstract: One of the most influential results in modern operator theory is that of Gelfand and Naimark, which, in the form most often presented, demonstrates a deep and fundamental connection between compact topological spaces and commutative unital C*-algebras. Outside of its intrinsic significance, the result is also notable for catalyzing an extensive research program to the ends of illuminating relations between operator algebras relevant to mathematical analysis and different sorts of spaces primarily studied by topologists, order theorists, and geometers of all walks of mathematics. This talk is an exposition on one such connection, that between operator algebras known as "commutative von Neumann algebras" and spaces known as "localizable measurable spaces"; we start with a brief review of abstract measure theory, introducing and motivating less well known concepts as we go, then use the new machinery to motivate and relate the aforementioned fragment of the theory of von Neumann algebras.
November 4, 2022
No meeting.
November 11, 2022
Speaker: José David Beltran (https://jdavidbel.github.io/)
Title: Applications of Young measures to scalar conservation laws
January 28, 2022
Organizational Meeting.
February 3, 2022
Speaker : Caleb Camrud
Title of Talk : Making Modal Logic Continuousus
Abstract : Modal language is used to model possibility, obligation, access to knowledge, and more. Logics of these modalities were then developed to reflect how we reason using modal language. But some modalities seem to exist in a continuum, rather than being discretely ordered. For a classic metaphysical example, it seems that the possible world in which I became a lawyer is more similar to the actual world than the possible world in which I am a frog. Indeed there intuitively seems to be an entire continuum of possible worlds "between" our actual world and the world in which I am a frog. As such, Dr. Ranpal Dosanjh (Iowa State University, Department of Philosophy) and I developed a method for making modal logic continuous. In this talk, I will present the syntax and semantics of basic modal logic, and discuss our method for constructing continuous modal logic.
February 10, 2022
Speaker : Jina Hyoungji Kim
Title of the Talk : Kolmogorov diffusion with Infinite-dimensional Brownian motion
Abstract : It is known that the Kolmogorov diffusion on a finite-dimensional space has the smooth density with respect to the Lebegue measure which is explicit. Now let us define the Kolmogorov diffusion on an infinite-dimensional space. Then we do not have a density of the heat kernel measure with respect to the Lebesgue measure anymore. But we can consider what is called quasi-invariance of a measure under some translation to obtain some type of smoothness of the heat kernel measure of an infinite-dimensional process.
February 17, 2022
Speaker : Kristina Moen
Title of the Talk : Growth of the Ulam Sequence: An Open Problem
Abstract : In his 1964 book “On Some Mathematical Problems Connected with Patterns of Growth Figures,” Stanislaw Ulam proposed an integer sequence with simple rules: the first two terms are 1 and 2 and each subsequent term is the smallest integer that can be uniquely written as the sum of two distinct earlier terms. This gives the sequence: 1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28… The first trillion Ulam numbers have been computed, but much about the sequence remains a mystery. The most common gap size between consecutive Ulam numbers is two, but gap sizes as large as 1,373 have appeared far into the sequence. Finding an upper bound on the gap size and growth rate remains an open question. Recently, there has been renewed interest into the sequence and its generalizations (s-Additive sequences) after Stefan Steinerberger discovered a “hidden signal” using Fourier series with Ulam numbers as frequencies. He found a persisting signal in the noise which gives rise a very regular distribution function. In this talk, we will delve into the world of Ulam numbers, what has been proven so far (including some surprising results when we choose different initial values), and possible avenues for further study.
February 24, 2022
Speaker : Chad Berner
Title of the Talk : Hilbert spaces of entire functions
Abstract : The Paley-Wiener space is a space of entire functions that are of exponential type and are square integrable on the real axis. It turns out that these entire functions are fourier transforms and show us the isometry of L^2 through the fourier transform. Furthermore, Louis de Branges generalized these spaces into Hilbert spaces of entire functions that are based off of entire functions of a more general sense than just exponentials. These generalized spaces also come equipped with nice properties such as results in function interpolation.
March 3, 2022
Speaker : Aniket Banerjee
Title of the Talk : Formulation of a mathematical model showing the dynamics of different biotypes of Soybean Aphids
Abstract : The soybean aphid, Aphis glycines (Hemiptera: Aphididae), is an invasive pest that can cause severe yield loss to soybeans in the northcentral United States. A tactic to counter this pest is the use of aphid-resistant soybean varieties. However, the occurrence of virulent biotypes can alter plant physiology and impair the use of this management strategy. Soybean aphids can alter soybean physiology primarily by two mechanisms, feeding facilitation and the obviation of resistance, favoring subsequent colonization by additional conspecifics. We developed a non-local, differential equation population model, to explore the dynamics of these biological mechanisms on soybean plants co-infested with virulent and avirulent aphids. We then use demographic parameters from laboratory experiments to perform numerical simulations via the model. These simulations successfully mimic various aphid dynamics observed in the field. Our model showed an increase in colonization of virulent aphids increases the likelihood that aphid-resistance is suppressed, subsequently increasing the survival of avirulent aphids, producing an indirect, positive interaction between the biotypes. These results suggest the potential for a "within plant" refuge that could contribute to the sustainable use of aphid resistant soybeans.
March 10, 2022
Speaker : Thomas Griffin
Title of the Talk : Icosystems – Modeling a Swarm
Abstract : Swarms are collections of loosely coupled distinct agents each following "simple" rules. Swarms do not use central coordination and individual agents need not be aware of the swarm’s overall function/goal. As each agent performs its task, the swarm collective can display unusual and unexpected emergent behaviors. For those swarms defying analytic evaluation, simulation remains as the only method to reveal these emergent behavior. A number of swarm behaviors will be demonstrated with different simple rules to follow, and then combined to discuss some more interesting dynamics and real world applications.
March 24, 2022
Speaker : Brian Zilli
Title of the Talk : Computable Blaschke Products
Abstract : We present some results of Matheson and McNicholl concerning the computability of Blaschke products and discuss the potential for further results on the computability of the set of accumulation points of Blaschke products.
March 31, 2022
Speaker : No Speaker
April 7, 2022
Speaker : Sarah McCarty
Title of the Talk : Image of Dual Ridgelet Transform
Abstract : We present results characterizing the image of the Dual Ridgelet Transform in the single variable case. The Dual Ridgelet Transform builds functions from a simple activation function and integration against compactly supported, signed, finite measures, which has applications in neural networks.
April 14, 2022
Speaker : Diego Rojas
Title of the Talk : From classical to computable: effectivizing objects and theorems in analysis
Abstract : Since the publication of Alan Turing's 1937 paper on the computable real numbers, mathematicians have looked for ways to adapt concepts found in mathematical analysis (and other fields) to a framework suitable for computation via a process called effectivization. Through effectivization, we are able to develop computable versions of theorems regarding objects such as real numbers, continuous real-valued functions, and measures. In this talk, I will be going over some examples of computable analogues to objects found in classical analysis, and I will explain how the effectivization process works in each instance. I will also give examples of computable versions of certain theorems from classical analysis.
April 21, 2022
Speaker : Yifan Hu
Title of the Talk : Stability analysis for spacetime Discontinuous Galerkin methods.
Abstract : Can we treat time as an additional dimension in solving time-dependent partial differential equations? What are the advantage and disadvantage of spacetime formulations for Discontinuous Galerkin methods? How do we know these numerical methods are stable? In this talk, we will try to answer these questions by inspecting Locally Implicit Discontinuous Galerkin (LIDG) methods and Regionally Implicit Discontinuous Galerkin (RIDG) methods, and share some common approaches to find the maximal timestep size that produces stable schemes.
April 28, 2022
Speaker : Evan Camrud
Title of the Talk : The Carleman matrix and iterated functions
Abstract : The Carleman matrix is a homomorphism (ALMOST a representation) mapping function composition into infinite matrices (hence why it's ALMOST a representation). We will introduce such matrices, their generalizations, and how they relate to calculating iterates of functions.
October 29, 2021
Organizational Meeting.
November 5, 2021
Speaker : Chad Berner
Title of the Talk : The Fragman-Lindelof Principle and a representation for some analytic functions in the upper half-plane.
Abstract : The maximum modulus theorem from complex analysis has a corollary called the Phragmen-Lindelof principle on simply connected sets due to analytic functions on these sets having a primitive, which is a result of Runge's theorem. This allows us to provide a representation of analytic functions on the upper half plane whose real part is non-negative with continuous extension to the closed half plane.
November 12, 2021
Speaker : Evan Camrud
Title of the Talk : Chaos: An Introduction
Abstract : This will be an introduction to chaos theory, broadly defined. We will cover definitions and examples of mixing, sensitivity to initial conditions, and strange attractors of nonlinear dynamical systems.
November 19, 2021
Speaker : Lee Przybylski
Title of the Talk : Measuring Effects of Starting Pitching
Abstract : Betting on baseball is challenging. One feature unique to the sport is that moneylines usually list probable starting pitchers. To take advantage of this, we develop a generalized linear mixed effects model using retrosheet data from several seasons. The model includes effects for teams, starting pitchers, and venue. Being able to assess a pitcher's performance independent of his team is also challenging. By estimating effects for each starting pitcher, fitting the model provides another way to measure a starting pitcher's effectiveness. In this talk we also provide some background on popular pitching metrics, such as ERA, FIP, and opponent WOBA, and compare these metrics to our estimated pitcher effects. As was done with FIP back in 2001, we also investigate how well these starting pitcher effects reflect an individual pitchers performance by looking at their correlation across seasons.
December 3, 2021
Speaker : Herionexy Mounier
Title of the Talk : Optimal Line Packings with Heisenberg Symmetry
Abstract : Zauner's Conjecture has been a subject of study in Frame Theory for several years. It states that for any complex Hilbert space of dimension d, there exists a d x d^2 equiangular tight frame (ETF). However, we proved a consequence of this conjecture by showing the existence of some particular ETFs. This was done by considering an orbit of some action of the Heisenberg group of a finite abelian group over the set of d x d matrices with complex entries. In this talk, I will introduce the concept of an ETF, together with the main result of this research.
December 10, 2021
Speaker : Brian Zilli
Title of the Talk : A Brief Introduction to Concepts in Computable Analysis
Abstract : We say that a real-valued function is ‘computable’ if there exists a computer program which, given a real number computed to a certain degree of precision, returns the function value to a desired degree of precision. We will define this concept rigorously, see some examples, and examine the interesting construction of a function which is computable and continuously differentiable but whose derivative is not computable.
January 21, 2020
Organizational Meeting.
January 28, 2020
Speaker : Mary Vaughan
Title of the Talk : Fractional powers of nondivergence form elliptic operators
Abstract : In this talk, we will show how to define fractional powers of nondivergence form differential operators in a pointwise and weak sense. We will then discuss some tools required to prove desired regularity estimates, such as Harnack inequality.
February 4, 2020
Speaker : Animesh Biswas
Title of the Talk : Decreasing Rearrangement and measure preserving transformation.
Abstract : In this talk, we will show how to define decreasing rearrangement of a measurable function. We will also define measure preserving transformation. Finally we will try to prove that in any finite measure space, a function can be written as a composition of its rearrangement and a measure preserving transformation.
February 11, 2020
Speaker : Manas Bhatnagar
Title of the Talk : Critical Thresholds in one dimensional Euler Poisson equations with non local forces.
Abstract : We will look at the existing critical threshold results in systems with nonlocal forces. We will see what makes the system complicated by adding a nonlocal term in the momentum equation. Lastly, we will also look at some open problems in this area.
February 18, 2020
Speaker : Nicole Buczkowski (University of Nebraska, Lincoln)
Title of the Talk : Local and Nonlocal Energy Minimization
Abstract : Today we will be going over some basics of the nonlocal framework and nonlocal operators. We will also go into the classical Euler-Lagrange equations as well as their nonlocal counterparts. We will further explore the growth conditions necessary for a minimizer of an energy functional to yield a weak solution to its corresponding Euler-Lagrange equation.
February 25, 2020
No talk.
March 3, 2020
Speaker : Evan Camrud
Title of the Talk : Some fixed point theorems and their applications.
Abstract : Fixed point theorems are some of the most general and widely-used theorems in analysis. They are consistently applied in differential equations, but have also found a foothold in discrete dynamical systems and functional analysis, namely in the invariant subspace problem. This talk will introduce some of the most common fixed point theorems, and give examples of them in applied mathematics.
March 10, 2020
Speaker : Hayley Olson (University of Nebraska, Lincoln)
Title of the Talk : Poincaré Inequalities in a Nonlocal Vector Calculus.
Abstract : The development of a nonlocal vector calculus rose out of the desire to describe standard systems of differential equations to discontinuous functions: this is pertinent in applications such as dynamic fracturing and image processing. This opened up a need to show well-posedness of systems with nonlocal calculus operators. In this talk, we introduce two nonlocal variations of the Poincaré inequality from Mikil Foss' Nonlocal Poincaré Inequalities for Integral Operators with Integrable Nonhomogeneous Kernels and discuss their use in showing well-posedness of systems with nonlocal operators.
March 17, 2020
No talk (Spring Break)
No seminar talk in the rest of the semester.
August 27, 2019
Organizational Meeting.
September 3, 2019
Speaker : Nathan Harding.
Title of the talk : The Kaczmarz Algorithm with Nonuniform Relaxation Parameters
Abstract : We modify the proof of Natterer for the relaxed Kaczmarz algorithm with nonuniform relaxation parameters. We show (1) that the Kaczmarz method converges to the solution of minimal norm if the system of equations is consistent and (2) that the Kaczmarz method converges to a parameter-dependent, weighted least squares solution if the system of equations is inconsistent. Our method further extends results for altered Kaczmarz algorithms. We also address randomized parameter selection. We end with some suggestive numerical experiments based on our method for further work in optimal parameter selection
September 10, 2019
Speaker : Animesh Biswas
Title of the talk : Regularity theory for nonlocal space-time master equations
Abstract : We analyze recent novel regularity theory for fractional power of parabolic operators in divergence form. These equations are fundamental in continuous time random walk models and appear as generalized Master equation. These equations are non-local in nature and were studied by Luis Caffarelli and Luis Silvestre. We developed a parabolic method of semigroups that allows us to prove a local extension problem. As a consequence we obtain interior and boundary Harnack inequalities and sharp interior and global parabolic Schauder estimates. For the latter, we also prove a characterization of the correct intermediate parabolic Hölder spaces in the spirit of Sergio Campanato. This is a joint work with Marta de Le´on-Contreras (Universidad Autonoma de Madrid, Spain) and Pablo Ra´ul Stinga (Iowa State University)
September 17, 2019
Speaker : Pranamesh Chakraborty
Title of the talk : Applications of trend filtering and maximum likelihood in traffic incident detection
Abstract : By 2020, the volume of traffic data is expected to rise to 11 petabytes, while a billion traffic cameras will be installed worldwide. This presentation will focus on using this wealth of information available from large-scale traffic data and closed-circuit television cameras towards developing an efficient automatic incident detection (AID) framework. First, a graph-based trend filtering method of AID framework will be introduced that can leverage large-scale traffic data along with the topology of the road network to learn the historical pattern. The second part of this presentation will focus on using maximum-likelihood estimation based semi-supervised learning technique to detect incidents from vehicle trajectories extracted from cameras. The results demonstrate that this framework can achieve superior performance in detecting such anomalies using these data sources and provide rapid incident responses.
September 24, 2019
Speaker : Wumaier Maimaitiyiming
Title of the talk : Fisher information regularization schemes for Wasserstein gradient flows.
Abstract : The variational scheme for computing Wasserstein gradient flows builds upon the Jordan–Kinderlehrer–Otto framework with the Benamou- Brenier’s dynamic formulation of the quadratic Wasserstein metric and adds a regularization by the Fisher information. This regularization can be derived in terms of energy splitting and is closely related to the Schrödinger bridge problem. It improves the convexity of the variational problem and automatically preserves the non-negativity of the solution. As a result, it allows us to apply sequential quadratic programming to solve the sub-optimization problem. We further save the computational cost by showing that no additional time interpolation is needed in the underlying dynamic formulation of the Wasserstein-2 metric, and therefore, the dimension of the problem is vastly reduced. This scheme can be allied to porous media equation, nonlinear Fokker-Planck equation, aggregation diffusion equation, and Derrida-Lebowitz-Speer-Spohn equation.
This is a paper I am reading recently, this paper starts with a general class of PDEs and reformulate the problem as a Wasserstein gradient flow, then introduces its variational formulation, finally solves the discrete minimization problem with the help of fisher information regularization.
October 1, 2019
Speaker : Mary Vaughan
Title of the talk : Viscosity Solutions of Elliptic Equations (Part 1)
Abstract : Following Luis Silvestre's notes on Viscosity Solutions of Elliptic Equations, we will provide an introduction to fully nonlinear PDEs and viscosity solutions.
October 8, 2019
Speaker : Lee Przybylski
Title of the talk : ATD Algorithms for Traffic Incident Detection and Ship Tracking
Abstract : ATD stands for "Algorithms for Threat Detection." The objective of the program is to develop new algorithms for analyzing spatiotemporal data sets. As part of this program, and in collaboration with Steven Harding, Paranamesh Chakraborty, and Eric Weber, we have developed various algorithms for detecting traffic incidents and tracking the paths of ships. This talk will discuss the details of developing and implementing those algorithms.
October 15, 2019
Speaker : Evan Camrud
Title of the talk : Not a proof of the Riemann hypothesis
Abstract : Solving one of the Millennium Prize Problems is hard, but that doesn't mean trying to can't be fun. This talk will be a brief survey of the Riemann zeta function, Mellin transform, and other special function theory, and will culminate in my latest attempt at tackling the Riemann hypothesis. (Spoiler: it didn't work.)
October 22, 2019
Speaker : Caleb Camrud
Title of the talk : A Brief Introduction to Continuous Logic
Abstract : While classical logic works well in formulating theories about discrete mathematical structures, its application to continuum-valued analytic structures is not very intuitive. Thus, in an attempt to more easily apply logical language and model theoretic results to analytic structures, continuous logic was invented. This introductory-level talk will not assume any background in logic, and will introduce the language of theories and deductions in classical logic before describing the corresponding notions in continuous logic.
October 29, 2019
Speaker : Makrand Khanwale
Title of the talk : Provably energy stability for second order time integration schemes for Cahn-Hilliard Navier Stokes equations
Abstract : I will talk about conservation laws (especially momentum transport) for single and multiphase flows. Starting with a brief introduction about various forms of momentum equations, I will present the generalisation to a specific two-phase formulation we use to simulate two-phase flows. We use a diffuse interface approach, which utilizes a thermodynamically consistent set of coupled Cahn Hilliard Navier-Stokes equations. I will talk about the strategy for proving energy stability of time integration schemes for such complicated operators with the example of a second order scheme in the semi-discrete form. I will also talk about the uniqueness of the advection-diffusion operator we use to track the interface in the Browder-Minty context.
November 5, 2019
Speaker : Mary Vaughan
Title of the talk : Viscosity Solutions of Elliptic Equations (Part 2)
Abstract : Continuing our discussion on Luis Silvestre's notes on Viscosity Solutions of Elliptic Equations, we will introduce some tools and techniques which are useful when working with viscosity solutions and then prove a comparison principle, an essential tool for uniqueness of solutions.
November 12, 2019
Speaker : Manas Bhatnagar
Title of the talk : On the energy estimates used to prove local existence in traffic flow model and hyperbolic balance laws
Abstract : We will take a look at the local existence and uniqueness results for a traffic flow model. To do critical threshold analysis (which is what I do), we need a little more than just existence. We need to know what goes wrong when the solution ceases to exist. One method is to derive energy estimates for the concerned physical quantities. We will prove these estimates. In the process, we will need some special Sobolev/Interpolation inequalities which I will prove (time permitting).
November 19, 2019 (at 12:10pm)
Speaker : Diego Rojas
Special week: Let's support Diego at his preliminary exam! More details to come.
November 26, 2019
No talk (Thanksgiving Break)
December 3, 2019
Speaker : Nyle Sutton
Title of the talk : Squaring the Circle: A Brief Discussion of Matrix Compression and the Story So Far
Abstract : Given two bounded linear operators A and B, which act on Hilbert spaces H and K, the relation between the numerical range inclusion relation W(B) ⊆ W(A) and the condition that B can be dilated to an operator of the form A⊗I is complex and nuanced. In this talk, I will discuss some known results in the area of Matrix Compressions and the applications of positive and completely positive maps to this question.
December 10, 2019
No talk.