We consider a class of solutions with pure impulse initial data below critical value such that within small time only librational-type waves are generated and the solutions should decay when |x| goes to infinity. In a neighbourhood of a certain gradient catastrophe point that contains both modulated plane waves and localized structures or ''spikes'', the asymptotic behaviour of the solutions can be universally described by analyzing a Riemann-Hilbert problem related to Painleve I equation Tritronquee solutions. It is a well-known fact that the solutions to Painleve equations have poles. In fact we show the locations of the poles are directly linked to where the ''spikes'' happen. In suitable scaling limit, we are able describe the first correction of the solution (compared to before breaking happens) using Painleve I Tritronquee solution away from the ''spikes''. I will explain how I want to then modify the Riemann-Hilbert problem to describe the ''spike'' shape. Notice that this is universal in the sense that the local asymptotics is not sensitive to the initial condition as long as it falls into a large class; it is only the space-time location of the transition that depends on the initial data. As a sidenote, the unique symmetry of the catastrophe location will also result in a symmetry of the corresponding Riemann-Hilbert problem, which allows us to describe the solution in more details. We lose this property when the initial condition is no longer an even function. Our technique is the Deift-Zhou steepest descent method related to an approach of universality for the focusing nonlinear Schrodinger equation. Speaker(s): Bingying Lu (University of Michigan)

]]>We discuss the Cohen-Lenstra heuristics from the point of view of counting unramified number field extensions of quadratic fields. This point of view admits a natural generalization of the setting of those heuristics, in which one can ask the same type of questions. We will focus on the specific case 2-group extensions of quadratic fields which has proven to be more tractable in recent years. We will put forth a conjecture about asymptotics and distributions of such extensions (beyond those considered by Cohen and Lenstra) and discuss our recent progress on this in the case of extensions with Galois groups which are central extensions of F_2 ^n by F_2. Speaker(s): Jack Klys (University of Toronto)

]]>Speaker(s): Bradley Zykoski (University of Michigan)

]]>In mathematical general relativity the Einstein equations describe the laws of the universe, giving the latter a geometric structure. This system of hyperbolic nonlinear partial differential equations (pde) has served as a playground for all kinds of new methods and results in pde analysis, geometry and other fields. A main goal in the study of these equations is to investigate the analytic and geometric properties of the solution spacetimes. Some of the most interesting solutions of the Einstein equations are spacetimes exhibiting gravitational radiation. A major breakthrough of general relativity happened in 2015 with LIGO's first detection of gravitational waves from black hole mergers. This marks the beginning of a new era, where these waves tell us about mathematical and physical properties of their sources. In this talk, I will first lay out some basics of mathematical general relativity, then we will delve into the mathematical description of gravitational radiation. Along the way, I will briefly highlight the Cauchy problem and the dynamics of black holes. Finally, I will explain some of our new results on how gravitational waves permanently change the spacetime. Speaker(s): Lydia Bieri (University of Michigan)

]]>Speaker(s): Angus Chung (UM)

]]>Measure-valued jump-diffusions provide useful approximations of large stochastic systems arising in finance, such as large sets of equity returns, limit order books, and particle systems with mean-field interaction. The dynamics of a measure-valued jump-diffusion is governed by an integro-differential operator of Levy type, expressed using a notion of derivative that is well-known from the superprocess literature, but different from the Lions derivative frequently used in the context of mean-field games. General and easy-to-use existence criteria for jump-diffusions valued in probability measures are derived using new optimality conditions for functions of measure arguments. Applications, beyond those mentioned above, include optimal control of measure-valued state processes. Speaker(s): Martin Larsson (ETH)

]]>Speaker(s): Sarah Koch (U(M))

]]>We will describe how the crystalline cohomology of a supersingular K3 surface gives rise to certain one-parameter families of K3 surfaces, which we call supersingular twistor spaces. Our construction relies on the unique behavior of the Brauer group of a supersingular K3 surface, as well as techniques coming from the study of the derived category and Fourier--Mukai equivalences. As applications, we find new proofs of Ogus's crystalline Torelli theorem and Artin's conjecture on the unirationality of supersingular K3 surfaces. These results are new in small characteristic. Speaker(s): Daniel Bragg (University of Washington)

]]>Speaker(s): Mel Hochster (University of Michigan)

]]>http://front.math.ucdavis.edu/1710.05278 Speaker(s): Mattias Jonsson (UM)

]]>The space \bar M_{g,n} is a compactification of the moduli space algebraic curves with marked points, obtained by allowing smooth curves to degenerate to nodal ones. We will talk about how the structure of its homology, H_i(\bar M_{g,n}), for n >> 0 is governed by an action of the category of finite sets and surjections. Speaker(s): Phil Tosteson (University of Michigan)

]]>Extreme magnetoconvection is the thermal convection in an electrically conducting fluid (for example, a liquid metal) that occurs in the presence of an imposed magnetic field. We analyze this phenomenon computationally with the focus on the case of very strong static fields (the Hartmann number up to 1E4) and strong heating (the Grashof number up to 1E12). Our goals are to understand the nature of the flow and to explore the implications for the design of liquid metal blankets of tokamak fusion reactors and other liquid metal systems. It is found that, as the intense Joule dissipation of induced electric currents suppresses conventional turbulence, the flows begin to demonstrate extreme, unusual and counter-intuitive behaviors, such as slow oscillation of remarkably high amplitudes, quasi-two-dimensional chaotic regimes, or exponentially growing elevator modes. Speaker(s): Oleg Zikanov (University of Michigan (Dearborn))

]]>Speaker(s): David Schwein (UM)

]]>Speaker(s): Nithin Varma (Boston University)

]]>In this work, we consider the soliton cellular automaton introduced in \cite{takahashi1990soliton} with a random initial configuration. We give multiple constructions of a Young diagram describing various statistics of the system in terms of familiar objects like birth-and-death chains and Galton-Watson forests. Using these ideas, we establish limit theorems showing that if the first $n$ boxes are occupied independently with probability $p\in(0,1)$, then the number of solitons is of order $n$ for all $p$, and the length of the longest soliton is of order $\log n$ for $p1/2$. Additionally, we uncover a condensation phenomenon in the supercritical regime: For each fixed $j\geq 1$, the top $j$ soliton lengths have the same order as the longest for $p\leq 1/2$, whereas all but the longest have order at most $\log n$ for $p>1/2$. As an application, we obtain scaling limits for the lengths of the $k^{\text{th}}$ longest increasing and decreasing subsequences in a random stack-sortable permutation of length $n$ in terms of random walks and Brownian excursions. Speaker(s): Hanbaek Lyu (Ohio State University)

]]>Speaker(s): Dimitri Liakakos (Sun Trading)

]]>A Hamiltonian formalism for integrable systems is a well-studied topic. Nevertheless, there is no approach which will cover all known examples integrable with the machinery of algebraic geometry. Very often there are no answers even to the simplest questions. We will formulate the main conjecture of the author regarding Poisson structures for these integrable systems. As an example, we consider the finite open Toda lattice. Speaker(s): Kirill Vaninsky (Michigan State University)

]]>Speaker(s): Jessica Fintzen (IAS)

]]>Speaker(s): TBA

]]>Speaker(s): Jasmine Powell (University of Michigan)

]]>Speaker(s): Yiwang Chen (UM)

]]>Martingale optimal transport (MOT), a version of the optimal transport (OT) with an additional martingale constraint on transportâ€™s dynamics, is an optimisation problem motivated by, and contributing to model-independent pricing problems in quantitative finance. Compared to the OT, numerical solution techniques for MOT problems are close to non-existent, relative to the theory and applications. In fact, the martingale constraint destroys the continuity of the value function, and thus renders any of the usual OT approximation techniques unusable. With Obloj, we proved that the MOT value could be approximated by a sequence of linear programming (LP) problems to which we apply the entropic regularisation. Further, we obtain in dimension one the convergence rate, which, to the best of our knowledge, is the first estimation of convergence rate in the literature. In the second part, we consider a semi-discrete Wasserstein distance of order 2, which could be solved by means of Voronoi diagram -- which is a static object in computational geometry. Inspired by a criterion in statistical physics, we may construct a sequence of probability distributions and we aim to show its convergence to some limit related to the minimal energy. Speaker(s): Gaoyue Guo (Oxford)

]]>Deciding whether a given algebraic variety is rational, or birational to projective space, is an age-old and challenging problem in algebraic geometry. The rationality problem for rationally connected varieties has seen incredible advances in the last several years, thanks to a degeneration method for the Chow group of 0-cycles initiated by Voisin, developed by Colliot-ThÃ©lÃ¨ne and Pirutka, and recently refined by Schreieder. After summarizing some of these advances, I will speak about joint work with Christian Boehning and Alena Pirutka on the rationality problem for two types of Fano fourfolds lying on the boundary of where different techniques are required: hypersurfaces of bidegree (2,3) in P^2 x P^3 and complete intersection of type (2,3) in P^6. The first have index 1 and Picard rank 2, and we prove that the very general such hypersurface is not stably rational by exploiting conic bundle and cubic surface bundle structures. The second have index 2 and Picard rank 1, and are more challenging. Speaker(s): Asher Auel (Yale University)

]]>Under what conditions do a group element and all of its conjugates form a generating set for the ambient group? Such an element is called a normal generator. For mapping class groups of surfaces, we give a number of geometric criteria that ensure that a mapping class is a normal generator. With these criteria in hand, we show that every nontrivial periodic element in a mapping class group (except for a hyperelliptic involution) is a normal generator. We also show that if the stretch factor of a pseudo-Anosov mapping class is sufficiently small, then it is a normal generator. Our pseudo-Anosov examples answer a question of Darren Long from 1986. This is joint work with Dan Margalit. Speaker(s): Justin Lanier (Georgia Tech)

]]>Speaker(s): Ilya Smirnov (University of Michigan)

]]>https://arxiv.org/abs/1710.04198 Speaker(s): Martin Ulirsch (UM)

]]>Fifty years after Zabusky and Kruskal's discovery of solitons, there still remain many fundamental open questions about nonlinear waves. This talk is devoted to two classical problems involving singular asymptotic limits: (i) the nonlinear stage of modulational instability and (ii) the small dispersion limit of (2+1)-dimensional systems. Modulational instability (MI), namely the instability of a constant background to long-wavelength perturbations, is a ubiquitous nonlinear phenomenon discovered in the 1960's. However, a characterization of the nonlinear stage of MI - namely, the behavior of solutions once the perturbations have become comparable with the background - was missing. In the first part of the talk I will describe recent work on this subject. I will first show how MI manifests itself in the inverse scattering transform for the focusing nonlinear Schroedinger (NLS) equation. Then I will characterize the nonlinear stage of MI by computing the long-time asymptotics of solutions of the NLS equation for localized perturbations of a constant background. For long times, the space-time plane divides into three regions: a left far field and a right far field, in which the solution is approximately constant, and a central region in which the solution is described by a slowly modulated traveling wave. Finally, I will show that this kind of behavior is not limited to the NLS equation, but instead it is shared by many different nonlinear models (including several PDEs, nonlocal systems and differential-difference equations). Regarding small-dispersion, in the 1960s, G.B. Whitham formulated a method that allows one to study the small-dispersion limit of a nonlinear PDE by deriving a set of hyperbolic PDEs describing the modulation of the parameters of the traveling-wave solutions of the original PDE. Whitham modulation theory, as is now called, has been subsequently generalized and applied with great success in a variety of settings. Most results, however, are limited to PDEs in one spatial dimension. In the second part of the talk I will show how one can formulate a (2+1)-dimensional generalization of Whitham modulation theory to derive the genus-1 Whitham modulation equations for a number of systems, including the Kadomtsev-Petviashvili (KP) equation, the two-dimensional Benjamin-Ono equation and a modified KP equation. I will discuss some basic properties of the resulting Whitham systems and I will show how these systems can be used to investigate many interesting questions about solutions of the original PDE, including the temporal dynamics of certain initial conditions and the transverse stability of genus-1 solutions. Speaker(s): Gino Biondini (State University of New York at Buffalo)

]]>Speaker(s): Will Dana (UM)

]]>Speaker(s): Eckhard Meinrenken (University of Toronto)

]]>A vector field is "Euler-like" with respect to a submanifold if its linear approximation is the Euler vector field on the normal bundle. We show that such a vector field canonically determines a tubular neighborhood embedding, and use this fact to discuss various normal form theorems in differential geometry. Examples range from Morse's lemma to various splitting theorems for singular foliations. Speaker(s): Eckhard Meinrenken (University of Toronto)

]]>Speaker(s): Saibal De (University of Michigan)

]]>Speaker(s): Nate Harman (University of Chicago)

]]>For a closed, strongly regular subset of the complex plane E of positive capacity and a non negative continuous weight w on E satisfying that the set where w is positive is of positive capacity, we prove that any weighted polynomial P_nw^n of degree at most n, n at least 1 satisfies that all points for which it attains its maximum on E live in the support of the weight w. If E is unbounded, we assume that w is of sufficient fast decrease with large argument. Examples are given to show that our requirements on E cannot in general be relaxed. As a consequence of this result we show that If E is a real interval of positive length, and p is a fixed positive number, we prove a necessary and sufficient condition which ensures that the Lp norm of P_nw^n on E is in an $n$th root sense, controlled by a corresponding discrete Lp Holder norm of P_nw^n on a certain well separated admissible triangular scheme of points $E_n$, n at least 1 of $E$. When P_nw^n is extremal on E_n, this condition implies results on zero distribution and zero location of P_nw^n on E. Speaker(s): Steven Damelin (Math Reviews)

]]>Speaker(s): David Zywina (Cornell University)

]]>Speaker(s): Mark Greenfield (University of Michigan)

]]>It is a classical problem to study whether any 2-dimensional Riemannian manifolds admit isometric embedding in the 3-dimensional Euclidean space. There are two versions of this problem, the local version and the global version. The local version was presented by Schlaefli in 1873 and is still open. In this talk, we review both versions of the problem and present some recent results. Speaker(s): Qing Han (Notre Dame University)

]]>Speaker(s): Jason Liang (UM)

]]>In this talk we present a family of new approximation methods for high-dimensional PDEs and BSDEs. A key idea of our methods is to combine multilevel approximations with Picard fixed-point approximations. Thereby we obtain a class of multilevel Picard approximations. Our error analysis proves that for semi-linear heat equations, the computational complexity of one of the proposed methods is bounded by $O(d\,\eps^{-(4+\delta)})$ for any $\delta > 0$, where $d$ is the dimensionality of the problem and $\eps\in(0,\infty)$ is the prescribed accuracy. We illustrate the efficiency of one of the proposed approximation methods by means of numerical simulations presenting approximation accuracy against runtime for several nonlinear PDEs from physics (such as the Allen-Cahn equation) and financial engineering (such as derivative pricing incorporating default risks) in the case of $d=100$ space dimensions. Speaker(s): Thomas Kruse (University of Duisburg-Essen)

]]>Speaker(s): David Anderson (Ohio-State University)

]]>Given any n points on a manifold, how can we systematically and continuously find a new point? What if we ask them to be distinct? In this talk, I will try to answer this question in surfaces. Then I will connect this question to sections of surface bundles. The slogan is "there is no center of mass on closed hyperbolic surfaces". Speaker(s): Lei Chen (University of Chicago)

]]>TBA Speaker(s): Lei Chen (University of Chicago)

]]>https://arxiv.org/abs/1710.08202 Speaker(s): Igor Dolgachev (UM)

]]>The numerical solution of hyperbolic conservation laws, either by Finite Volume or Finite Element methods, rests largely on representing the solution by smooth basis functions within each element, leaving discontinuities at the boundaries. The discontinuities are resolved by solving one-dimensional Riemann problems. The basic idea was introduced by Godunov in 1959, and since then has been accepted as a natural, almost inevitable, approach. In this talk, the representations will be continuous and no Riemann problems will be solved. The emphasis will be on distinctive handling of the advective and non-advective disturbances, with initial reference to the advective-acoustic structure of the Euler equations. In the usual approach, this distinction is not given prominence, because in one dimension the advective and acoustic modes behave very similarly. Here, we recognize the considerable differences found in higher dimensions. Advection is dealt with by semi-Lagrangian Streamline tracing, and acoustics by adapting Poisson's solution to the Initial-Value Problem for the scalar wave equation. These elements are combined to give a third-order accurate, fully explicit, maximally stable and conservative method. Initial experiments suggest that it provides accuracy comparable to other high-order methods at substantially reduced cost. Speaker(s): Phil Roe (University of Michigan, Aerospace Engineering)

]]>Speaker(s): Krystal Taylor (OSU)

]]>Speaker(s): Haoyang Guo (UM)

]]>Speaker(s): Emanuel Gull (University of Michigan)

]]>Speaker(s): Eric Ramos (University of Michigan)

]]>Speaker(s): Peter Miller (University of Michigan)

]]>Speaker(s): Chris Hall (Western University)

]]>[This session may take place on 2/12 or 2/19.] Speaker(s): TBA

]]>Speaker(s): Salman Siddiqi (University of Michigan)

]]>Minimal surfaces are ubiquitous in Geometry but they are quite hard to find. For instance, Yau in 1982 conjectured that any 3-manifold admits infinitely many closed minimal surfaces but the best one knows is the existence of at least two. In a different direction, Gromov conjectured a Weyl Law for the volume spectrum that was proven last year by Liokumovich, Marques, and myself. I talk about my recent work with Irie, Marques, and Song where we combined Gromovâ€™s Weyl Law with the Min-max theory Marques and I have been developing over the last years to prove that, for generic metrics, not only there are infinitely many minimal hypersurfaces but they are also dense and equidistributed . I will cover the history of the problem and try address the main ideas without being technical. Speaker(s): Andre Neves (University of Chicago)

]]>Speaker(s): David Schwein (UM)

]]>Martingale Optimal Transport and Skorokhod Embedding Problems are naturally studied alongside their dual problems, also known as Robust Hedging Problems. I will explore the question of Strong Duality, i.e. the absence of a duality gap and existence of a dual optimizer, in both discrete and continuous time. In particular I will discuss how the choice of the dual domain can affect Strong Duality and how the existence of a dual optimizer allows for an easy derivation of Monotonicity Principles. Speaker(s): Florian Stebegg (Columbia University)

]]>Speaker(s): Ana-Maria Castravet (Northeastern University)

]]>Speaker(s): Hannah Alpert (Ohio State University)

]]>http://front.math.ucdavis.edu/1710.05331 Speaker(s): Takumi Murayama (UM)

]]>"Of all the systems in statistical mechanics on which exact calculations have been performed, the two-dimensional Ising model is not only the most thoroughly investigated; it is also the richest and most profound." These are the opening lines in Barry McCoy's and Tai Tsun Wu's classical 1973 monograph and since then several new features of the model have been discovered. In this (semi)-review lecture we will first familiarize ourselves with a few classical aspects of the model: the one-dimensional version, Peierls's argument for the spontaneous magnetization, Onsager's, Kaufmann's and Yang's remarkable exact computations and the analysis of spin-spin correlation functions due to Cheng and Wu. After that we shall discuss the massive scaling limit of the same correlation functions and highlight the appearance of Painleve-III and Painleve-VI functions as discovered in the works of Barouch, McCoy, Tracy, Wu, Jimbo and Miwa in 1976 - 1980. Our lecture will conclude with the speaker's recent introduction (arXiv:1710.04295) of Hamiltonian action integral methods in the scaling analysis of the model. This talk is intended for a broad math and physics audience in particular including students. Speaker(s): Thomas Bothner (University of Michigan)

]]>Speaker(s): Devlin Mallory (UM)

]]>Speaker(s): Evita Nestoridi (Princeton)

]]>Speaker(s): AVAILABLE

]]>Speaker(s): Elizaveta Rebrova (University of Michigan)

]]>For any k >= 1, we study the distribution of the difference between the number of integers n Speaker(s): Xianchang Meng (McGill University)

]]>Speaker(s): Kostas Tsouvalas (University of Michigan)

]]>Shimura varieties are quotients of hermitian symmetric domains by arithmetic groups. They generalize the classical elliptic modular curves, are defined over number fields and play a central role in number theory and the Langlands program. I will discuss some classical work and more recent progress on the problem of describing the structure of some of these varieties over the integers and, in particular, their reductions modulo primes. Speaker(s): George Pappas (Michigan State University)

]]>Speaker(s): Trevor Hyde (UM)

]]>We study the problem of maximizing expected utility of terminal wealth for an investor facing a mix of constant and proportional transaction costs. While the case of purely proportional transaction costs is by now well understood and existence of optimal strategies is known to hold for a very general class of price processes, the case of constant costs remains a challenge since the existence of optimal strategies is not even known in tractable models (such as, e.g., the Black-Scholes model). In this talk, we present a novel approach which allows us to construct optimal strategies in a multidimensional diffusion market with price processes driven by a factor process and for general lower-bounded utility functions. One of the main challenges for the problem under consideration is that the value function turns out to be piecewise but not globally continuous. We establish this result in two steps: (1) We apply the stochastic Perron's method to show that the value function is a discontinuous viscosity solution of the associated dynamic programming PDE (a nonlocal parabolic free boundary problem). (2) We establish a local comparison principle for viscosity solutions of this PDE, which implies uniqueness of the value function as well as piecewise continuity. Having established piecewise continuity, we use a characterization of the value function as the pointwise infimum of a suitable set of superharmonic functions to construct optimal trading strategies. The advantage of this approach is that the pointwise infimum (i.e. the value function) inherits the superharmonicity property, which in turn allows us to prove a verification theorem for candidate optimal strategies requiring only piecewise continuity of the value function. An application of the verification theorem entails the existence of optimal strategies. In particular, to the best of our knowledge, our approach leads to the first uniqueness result for discontinuous viscosity solutions of nonlocal PDEs and the model is a rare example of a stochastic control with a discontinuous value function which can be solved completely. This talk is based on joint work with SÃ¶ren Christensen (University of Hamburg). Speaker(s): Christoph Belak (University of Trier)

]]>Speaker(s): Alex Perry (Columbia University)

]]>Speaker(s): Irena Swanson (Reed College)

]]>https://arxiv.org/abs/1711.09225 Speaker(s): Emanuel Reinecke (UM)

]]>Speaker(s): Eric Keaveny (Imperial College)

]]>Speaker(s): Sanal Shivaprasad (UM)

]]>Speaker(s): Scott Rich (University of Michigan)

]]>Speaker(s): No Talk (Spring Break)

]]>Speaker(s): Winter Break

]]>TBA

]]>Speaker(s): UjuÃ© Etayo (Universidad de Cantabria (Spain))

]]>Mean field games (MFG) are dynamic games with infinitely many infinitesimal agents. In this joint work with C. Rainer, we study the efficiency of Nash MFG equilibria: Namely, we compare the social cost of an MFG equilibrium with the minimal cost a global planner can achieve. We find a structure condition on the problem under which there exists efficient MFG equilibria and, in case this condition is not fulfilled, quantify how inefficient MFG equilibria are. Speaker(s): Pierre Cardaliguet (Paris Dauphine)

]]>Speaker(s): Marty Weissman (UC Santa Cruz)

]]>Speaker(s): TBA

]]>Speaker(s): Montek Gill (University of Michigan)

]]>Speaker(s): Selim Esedoglu (University of Michigan)

]]>Speaker(s): David Treumann (Boston College)

]]>https://arxiv.org/abs/1708.08506 Speaker(s): Haoyang Guo (UM)

]]>Speaker(s): Michael Shelley (New York University/Flatiron Institute)

]]>Speaker(s): Jason Liang (UM)

]]>Speaker(s): Tyler Bolles (University of Michigan)

]]>Speaker(s): Dimitrios Ntalampekos (UCLA)

]]>Speaker(s): Vinayak Vatsal (UBC)

]]>Speaker(s): Didac Martinez-Granado (Indiana University)

]]>Speaker(s): Rohini Ramadas (Harvard University)

]]>Rational self-maps of the complex projective plane have long been of interest in algebraic geometry. They're also quite interesting from a dynamical point of view. The dynamical complexity of a rational map is governed by the degrees of the polynomials that define it and its iterates. In general, however, it's very hard to understand how these degrees behave as the iterate increases. I will spend my talk explaining the connection between degrees and dynamics, surveying what we do and don't know, and pointing to some interesting connections with other pieces of mathematics. Speaker(s): Jeff Diller (Notre Dame University)

]]>Speaker(s): Dan Thompson (The Ohio State University)

]]>Speaker(s): Jacob Haley (UM)

]]>Speaker(s): Hao Xing (LSE)

]]>TBA

]]>http://front.math.ucdavis.edu/1703.07505 Speaker(s): Harold Blum (UM)

]]>Speaker(s): AVAILABLE

]]>Speaker(s): Dan Thompson (The Ohio State University)

]]>Speaker(s): Ben Krakoff (UM)

]]>Speaker(s): Bikash Kanungo (University of Michigan)

]]>Speaker(s): Nyima Kao (UChicago)

]]>TBA

]]>TBA Speaker(s): Vilma Mesa (Univ Michigan School of Education)

]]>Speaker(s): Nicholas Wawrykow (University of Michigan)

]]>Speaker(s): Richard Taylor (Institute for Advanced Study, Princeton)

]]>Speaker(s): Yifeng Huang (UM)

]]>TBA

]]>Speaker(s): Johanna Mangahas (University at Buffalo)

]]>http://front.math.ucdavis.edu/1710.04364 Speaker(s): Kannappan Sampath (UM)

]]>Speaker(s): AVAILABLE

]]>Speaker(s): Cagatay Kutluhan (SUNY Buffalo)

]]>Speaker(s): Nancy Wang (UM)

]]>Speaker(s): Amanda Bower (University of Michigan)

]]>Speaker(s): Madeline Brandt (UC Berkeley)

]]>Speaker(s): Emily Burkhead (Duke)

]]>Speaker(s): Brian Smithling (Johns Hopkins University)

]]>Speaker(s): Maxime Scott (Indiana University)

]]>Speaker(s): Xiaojun Huang (Rutgers University)

]]>Speaker(s): Alex Horawa (UM)

]]>Speaker(s): Daniel Litt (Columbia University)

]]>We describe a new algorithm which determines if the intersection of a quasiconvex subgroup of a negatively curved group with any of its conjugates is infinite. The algorithm is based on the concepts of a coset graph and a weakly Nielsen generating set of a subgroup. We also give a new proof of decidability of a membership problem for quasiconvex subgroups of negatively curved groups. Speaker(s): Rita Gitik (UM)

]]>https://arxiv.org/abs/1801.01046 Speaker(s): Zili Zhang (UM)

]]>Speaker(s): AVAILABLE

]]>Speaker(s): Attilio Castano (UM)

]]>Speaker(s): Dejiao Zhang (University of Michigan)

]]>Speaker(s): Bruce Sagan (Michigan State University)

]]>TBA

]]>Speaker(s): TBA

]]>Speaker(s): Samantha Pinella (University of Michigan)

]]>Speaker(s): Nizar Touzi (Ecole Polytechnique, France)

]]>Speaker(s): Nizar Touzi (Ecole Polytechnique)

]]>Speaker(s): Akhil Mathew (University of Chicago)

]]>Speaker(s): Nizar Touzi (Ecole Polytechniqie)

]]>Speaker(s): Paolo Mantero (University of Arkansas)

]]>Speaker(s): Fritz Gesztesy (Baylor University, Waco TX)

]]>https://arxiv.org/abs/1712.04367 Speaker(s): Matt Stevenson (UM)

]]>Interacting excitatory and inhibitory neuronal populations often generate oscillations in electrical fields in the brain. I will briefly review this mechanism and the reasons to believe that it is important in brain function. Most of the talk will be focused on the effects of recurrent excitation, i.e., of the neurons of a local network in the brain exciting each other. Recurrent excitation can sustain activity in a network that would otherwise be quiescent; this is believed to be the basis of working memory. It can also lead to a runaway process, with excitation generating more excitation etc., much as the presence of a quadratic term on the right-hand side of a differential equation can lead to blow-up in finite time; this may be related to epileptic seizures. For model problems, we prove that abrupt transitions to runaway activity require recurrent excitation with fast kinetics, while working memory activity is more robust with recurrent excitation with slow kinetics. Speaker(s): Christoph Borgers (Tufts University)

]]>Speaker(s): Emanuel Reinecke (UM)

]]>Speaker(s): Matthew Kvalheim (University of Michigan)

]]>Speaker(s): Neriman Tokcan (University of Michigan)

]]>Speaker(s): Jeffrey Adams (Univ of Maryland)

]]>Speaker(s): Feng Zhu (University of Michigan)

]]>Can we make objects invisible? This has been a subject of human fascination for millennia in Greek mythology, movies, science fiction, etc. including the legend of Perseus versus Medusa and the more recent Star Trek and Harry Potter. In the last decade or so there have been several scientific proposals to achieve invisibility. We will introduce some of these in a non-technical fashion concentrating on the so-called "transformation optics" that has received the most attention in the scientific literature. Speaker(s): Gunther Uhlmann (University of Washington)

]]>We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also several applications in optics and medical imaging among others. The problem can be recast as a geometric problem: Can one determine the Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform. We will also describe some recent results, join with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed. Speaker(s): Gunther Uhlmann (University of Washington)

]]>Speaker(s): Jeff Danciger (U Texas)

]]>Speaker(s): Jianfeng Zhang (USC)

]]>Speaker(s): Zili Zhang (UM)

]]>We consider inverse problems for the Einstein equation with a time-depending metric on a 4-dimensional globally hyperbolic Lorentzian manifold. We formulate the concept of active measurements for relativistic models. We do this by coupling Einstein equations with equations for scalar fields. The inverse problem we study is the question of whether the observations of the solutions of the coupled system in an open subset of the space-time with the sources supported in this set determines the properties of the metric in a larger domain. To study this problem we define the concept of light observation sets and show that knowledge of these sets determine the conformal class of the metric. This corresponds to passive observations from a distant area of space which is filled by light sources. We will start by considering inverse problems for scalar non-linear hyperbolic equations to explain our method. No previous knowledge of Lorentzian geometry or general relativity will be assumed. This is joint work with P. Hinz, Y. Kurylev, M. Lasss and Y. Wang. Speaker(s): Gunther Uhlmann (University of Washington)

]]>Speaker(s): TBA TBA (TBA)

]]>Speaker(s): Michael Weinstein (Columbia University)

]]>Speaker(s): Jason McCullough (Iowa State University)

]]>Speaker(s): Karen Smith (UM)

]]>Speaker(s): Kevin Hannay (Schreiner University)

]]>Speaker(s): Fanny Kassel (IHES)

]]>Speaker(s): Shubhodip Mondal (UM)

]]>We'll be celebrating the achievements of our graduating students! Graduating applied math (or applied math adjacent) students will give short descriptions of their thesis work and discuss what's next for them! Speaker(s): Graduating students (University of Michigan)

]]>Speaker(s): Giulio Tiozzo (Toronto)

]]>TBA

]]>Speaker(s): TBA

]]>Speaker(s): Mitul Islam (University of Michigan)

]]>Speaker(s): Jacob Tsimerman (University of Toronto)

]]>Speaker(s): Maxim Bichuch (Johns Hopkins)

]]>https://arxiv.org/abs/1712.09487 Speaker(s): Shubhodip Mondal (UM)

]]>Speaker(s): Adam Larios (University of Nebraska)

]]>Speaker(s): Walter Schachermayer (University of Vienna)

]]>Speaker(s): Walter Schachermayer (University of Vienna)

]]>Speaker(s): Walter Schachermayer (University of Vienna)

]]>Speaker(s): Daniel Lathrop (University of Maryland)

]]>Speaker(s): Saverio Spagnolie (University of Wisconsin)

]]>Speaker(s): Aravind Asok

]]>Speaker(s): Benjamin Akers (Air Force Institute of Technology)

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