TBA

]]>Speaker(s): Ben Dozier (Stony Brook)

]]>Speaker(s): Fall Break

]]>Speaker(s): Haoyang Guo (University of Michigan)

]]>Newton polygons provide us with a tool for understanding roots of polynomials and studying irreducibility. In this talk, I'll give some examples of successful applications of Newton polygons and also discuss their limitations. Speaker(s): Lara Du (UM)

]]>The Grothendieck group of varieties over a field k is the quotient of the free abelian group of isomorphism classes of varieties over k by the so-called cut-and-paste relations. It moreover has a ring structure coming from the product of varieties. Many problems in number theory have a natural, more geometric counterpart involving elements of this ring. Thus, Poonenâ€™s Bertini theorem over finite fields has a motivic analog due to Vakil and Wood, which expresses the motivic density of smooth hypersurface sections as the degree goes to infinity in terms of a special value of Kapranovâ€™s zeta function. I will report on recent joint work with Sean Howe, where we prove a broad generalization of Vakil and Woodâ€™s result, which implies in particular a motivic analog of Poonenâ€™s Bertini theorem with Taylor conditions, as well as motivic analogs of many generalizations and variants of Poonenâ€™s theorem. A key ingredient for this is a notion of motivic Euler product which allows us to write down candidate motivic probabilities. Speaker(s): Margaret Bilu (New York University)

]]>I will talk about joint work of Athreya, Lalley, Wroten and myself. Given a hyperbolic surface S, a typical long geodesic arc will divide the surface into many polygons. We give statistics for the geometry of a typical tessellation. Along the way, we look at how very long geodesic arcs behave in very small balls on the surface.

Speaker(s): Jenya Sapir (SUNY Binghamton)

TBA Speaker(s): Devlin Mallory (University of Michigan)

]]>When G is a reductive (non-compact) Lie group, one can consider automorphic forms for G. These are functions on the locally symmetric space X_G associated to G that satisfy some sort of nice differential equation. When X_G has the structure of a complex manifold, the _modular forms_ for the group G are those automorphic forms that correspond to holomorphic functions on X_G. They possess close ties to arithmetic and algebraic geometry. For certain exceptional Lie groups G, the locally symmetric space X_G is not a complex manifold, yet nevertheless possesses a very special class of automorphic functions that behave similarly to the holomorphic modular forms above. Building upon work of Gan, Gross, Savin, and Wallach, I will define these modular forms and explain what is known about them. Speaker(s): Aaron Pollack (Duke University)

]]>The structure of social networks reflects important social processes, such as status, communities, and inequality---but separating signal from noise is nontrivial in social data. Statistical inference provides one point of entry: unpacking the assumptions behind random graph models, we can understand what tools will help us uncover meaningful social structure from noise. The empirical design of networks problems, however, is often overlooked but fundamentally changes the space of problems available. I will discuss single-graph (N=1) problems and some of the surprising challenges behind many-graph (N >> 1) problems. Using random graph models, statistical inference, and empirical design, I will present a brief overview of how to understand networked processes in real systems---from families and firms to food webs and Facebook. Speaker(s): Abbie Jacobs (University of Michigan, School of Information and Complex Systems)

]]>

The Shapiro-Shapiro conjecture states the following. Let f : P^1 to P^n be any map. If all inflection points of the map (roots of the Wronskian of f) are all real, then the map itself can, after change of coordinates, be defined over R with real polynomials.

An equivalent statement is that certain real Schubert varieties in the Grassmannian intersect transversely -- a fact with broad combinatorial and topological consequences. The conjecture, made in the 90s, was proven by Mukhin-Tarasov-Varchenko in '05/'09 using methods from quantum mechanics.

I will present a proof of a generalization of the Shapiro-Shapiro conjecture, allowing the Wronskian to have complex conjugate pairs of roots. We decompose the real Schubert cell according to the number of such roots, and define an orientation of each connected component. For each part of this decomposition, we prove that the topological degree of the restricted Wronski map is an evaluation of a symmetric group character. In the case where all roots are real, this implies that the restricted Wronski map is a topologically trivial covering map; in particular, this gives a new proof of the Shapiro-Shapiro conjecture.

This is joint work with Kevin Purbhoo. Speaker(s): Jake Levinson (University of Washington)

A theorem of ErdÅ‘s and Rado generalizes Ramsey's theorem to

infinite cardinals: for each cardinal n, there exists a cardinal N so

that each graph with N vertices contains either a clique or an

independent set of size n. In the infinite case, one can take n = N if n

is countable but in most other uncountable cases N must be much bigger

than n. Stability theory is a branch of model theory studying certain

definability conditions allowing us to take n = N for a large number of

infinite cardinals. Historically, stability theory was first developed

by Shelah for classes axiomatized by a first-order theory. In this talk,

I describe a generalization to a large class of categories, accessible

categories. I will also talk about recent progress on the eventual

categoricity conjecture, resolved by Morley and Shelah for first-order

but still open for accessible categories. Speaker(s): Sebastien Vasey (Harvard University)

Speaker(s): John Hubbard (Cornell/Marseille)

]]>Speaker(s): Yutong Li

]]>Speaker(s): Sayantan Khan (UM)

]]>Speaker(s): Michal Zydor (University of Michigan)

]]>Any plane rational self-map f:P^2->P^2 has an 'algebraic degree' defined to be the common degrees of its components in homogeneous coordinates. The sequence (deg f^n) always grows like a power L^n of some number L, the 'dynamical degree', which is a fundamental invariant for the dynamics of f. The dynamical degree is (in some sense) typically an integer, equal to the degree of f, and there are only countably many possibilities for its value in general. Nevertheless, I will describe joint work with Jason Bell and Mattias Jonsson in which we give a specific example where the first dynamical degree turns out to be a transcendental number. Speaker(s): Jeffrey Diller (University of Notre Dame)

]]>We study the relative Gromov-Witten theory on T*P^1 \times P^1 and show that certain equivariant limits give us the relative invariants on P^1\times \P^1. By formulating the quantum multiplications on Hilb(T*P^1) computed by Devash Maulik and Alexei Oblomkov as vertex operators and computing the product expansion, we demonstrate how to get the insertion and tangency operators computed by Yaim Cooper and Rahul Pandharipande in the equivariant limits. Speaker(s): Shuai Wang (Columbia University)

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

]]>Speaker(s): Isabel Vogt (Stanford University)

]]>Speaker(s): Yueqiao Wu (University of Michigan)

]]>Speaker(s): Yunus Zeytuncu (University of Michigan-Dearborn)

]]>Following lecture 6 and 7 from http://www.math.harvard.edu/~lurie/252x.html. Speaker(s): Shubhodip Mondal (UM)

]]>Speaker(s): Eric Canton (University of Michigan Ann Arbor)

]]>Speaker(s): Harry Richman (UM)

]]>I will discuss the topology of a space of stable tropical curves of genus g with volume 1. The reduced rational homology of this space is canonically identified with the top weight cohomology of M_g and also with the homology of Kontsevich's graph complex. As one application, we show that H^{4g-6}(M_g) grows exponentially with g. This disproves a recent conjecture of Church, Farb, and Putman as well as an older, more general conjecture of Kontsevich. As another application, we prove a formula conjectured by Zagier for the S_n-equivariant top weight Euler characteristic of M_{g,n}.

Based on joint work with M. Chan, C. Faber, and S. Galatius. Speaker(s): Sam Payne (University of Texas at Austin)

Speaker(s): Angela Maennela (University of Michigan)

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

]]>For a K3 surface X over a number field with potentially good reduction everywhere, we prove that there are infinitely many primes modulo which the reduction of X has larger geometric Picard rank than that of the generic fiber X. A similar statement still holds true for ordinary K3 surfaces over global function fields. In this talk, I will present the proofs via the intersection theory on GSpin Shimura varieties and also discuss various applications. These results are joint work with Ananth Shankar, Arul Shankar, and Salim Tayou and with Davesh Maulik and Ananth Shankar. Speaker(s): Yunqing Tang (IAS)

]]>Speaker(s): Aaron Calderon (Yale)

]]>Speaker(s): Aaron Calderon (Yale)

]]>TBA Speaker(s): Zhan Jiang (University of Michigan)

]]>Speaker(s): Shizhang Li (UM)

]]>Mark Schmude is a graduate of the University of Michigan's Master of Science in Financial Engineering program. He current works for MSCI in Ann Arbor as Executive Director of Client Coverage. Along with a representative from MSCI's human resources team, Mark will talk to Quant students about his career path in quantitative finance and how they can prepare for the job market. Speaker(s): Mark Schmude (MSCI)

]]>Speaker(s): Hanliang Guo (University of Michigan)

]]>For any finite real reflection group W, Chapoton defined three polynomials enumerating combinatorial objects associated with W: the F-triangle F(x,y), the H-triangle H(x,y), and the M-triangle M(x,y). In particular, F(x,y) enumerates faces of the cluster complex associated with W. Chapoton conjectured certain identities satisfied by F(x,y) and H(x,y) and by F(x,y) and M(x,y), which were later proved by Thiel and Athanasiadis, respectively. We present analogues of these three polynomials given the initial data of a nonkissing complex in the sense of Petersen, Pylyavskyy, and Speyer. The cluster complex associated with the symmetric group is a special case of the nonkissing complex. We prove the analogue of Chapoton's F(x,y) and H(x,y) identity and conjecture the analogue of his F(x,y) and H(x,y) identity. This joint work with Thomas McConville.

Speaker(s): Alexander Garver (University of Michigan)

Speaker(s): Ben Schmidt (MSU)

]]>From blood flow to subsurface flows, particulate flows are ubiquitous. Direct numerical simulations of dense particle suspensions in viscous fluids, governed by Stokes equations, are extremely challenging yet critically important to bring insights into their macro-scale flow behavior. We will give an overview of research conducted by current (and past) graduate students in our department that helped overcome several computational bottlenecks in these problems using tools from complex analysis, potential theory, PDEs and numerical analysis. We will discuss how these methods can be useful in the design of microfluidic chips, shape optimization and in understanding the complex physics of soft particulate flows. Speaker(s): Shravan Veerapaneni (Michigan)

]]>https://arxiv.org/abs/1711.06456 Speaker(s): Bogdan Zavyalov (Stanford/UM)

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

]]>Speaker(s): Aidan Herderschee (UM)

]]>Speaker(s): Yulia Bibilo (IITP RAS)

]]>Speaker(s): Jakob Hultgren (University of Maryland)

]]>Speaker(s): Carsten Sprunger (UM)

]]>We consider complete analytic Riemannian manifolds of bounded nonpositive curvature. Theseinclude locally symmetric and, in particular, arithmetic manifolds, the study of which is stronglyrelated to the theory of lattices and arithmetic groups. The complexity of such manifoldsis controlled by the volume. This phenomenon can be measured in terms of the growth oftopological, geometric, algebraic, arithmetic and representation theoretic invariants. The Gauss-Bonnet theorem implies that the topology of a closed constant curvature surfaceis determined by the volume. In general dimension and varied curvature, a classical theoremof Gromov says that the Betti numbers are bounded by the volume. In recent years, there hasbeen a growing interest in the size of the torsion part of the homology, motivated by applicationsin number theory. Many invariants can be controlled by obtaining an efficient triangulation ora simplicial realization (or approximation). In analogy to asymptotic group theory, one line ofproblems concerns the growth of the number of manifolds of a certain type. A main tool is the emerging theory of invariant random subgroups, which is extremely efficient forthe analysis of the asymptotic behavior of certain analytic invariants as well as for some uniformresults. Speaker(s): Tsachik Gelander (Weizmann Institute of Science)

]]>TBA

]]>Speaker(s): Rishi Sonthalia (University of Michigan)

]]>Following lecture 8 and 9 from http://www.math.harvard.edu/~lurie/252x.html. Speaker(s): Yunze Lu (UM)

]]>Details about the Learning Community may be found at

http://www.math.lsa.umich.edu/~glarose/dept/teaching/lcit.html . Speaker(s): LCIT Discussion

Speaker(s): Sridhar Venkatesh (University of Michigan Ann Arbor)

]]>Speaker(s): Malavika Mukundan (UM)

]]>In this talk, I will discuss what is meant by â€œquantum symmetryâ€ from the algebraic viewpoint of actions and coactions on algebras. The term â€œquantumâ€ is used as algebras are allowed to be noncommutative here, say to include deformations of coordinate rings of varieties. I will mention some interesting results on when actions on algebras must factor or do not factor through actions of classical gadgets (such as groups or Lie algebras), that is, when we must enter the realm of quantum groups (or Hopf algebras) to understand symmetries of a given algebra. This all fits neatly into the framework of studying algebras in monoidal categories, and if time permits, I will give some recent results in this direction. I aim to keep the level of the talk down-to-earth by including many basic definitions and examples. Speaker(s): Chelsea Walton (University of Illinois)

]]>TBA Speaker(s): William Clark (University of Michigan)

]]>Speaker(s): Yunze Lu (University of Michigan)

]]>Speaker(s): Zhou Fang (UM)

]]>Speaker(s): Harold Blum (University of Utah)

]]>Tontines offer a great alternative to current pension products.

Members invest in a financial market and receive an additional stream of income from passed away peers.

But, like annuities, tontines suffer from pensioners' reluctance to fund the additional stream by giving up wealth at death.

Promoting tontines, we analyze the effect of a bequest motive on the decision to invest in a tontine.

We formulate an investment problem where a pensioner chooses the percentage of wealth in the tontine, an investment strategy and their consumption rate.

The investment problem is formulated such that the optimal strategy maximizes the utility of lifetime consumption and the left behind bequest.

We show that, for a risk-averse investor, the optimal fixed percentage in the tontine is around $80\%$ for a wide range of risk aversion and different bequest motives.

We present the case of a flexible percentage together with a discussion about its suitability together with how we attempt to solve its issues. Speaker(s): Thomas Bernhardt (UM)

With the invention of lasers, the intensity of a light wave was increased by orders of magnitude over what had been achieved with a light bulb or sunlight. This much higher intensity led to new phenomena being observed, such as violet light coming out when red light went into the material. After Gérard Mourou and I developed chirped pulse amplification, also known as CPA, the intensity again increased by more than a factor of 1,000 and it once again made new types of interactions possible between light and matter. We developed a laser that could deliver short pulses of light that knocked the electrons off their atoms. This new understanding of laser-matter interactions, led to the development of new machining techniques that are used in laser eye surgery or micromachining of glass used in cell phones.

You may find more details: lsa.umich.edu/physics/special-lecture

Speaker(s): Sara Maloni (University of Virginia)

]]>Speaker(s): Jakub Witaszek (UM)

]]>Information Geometry is the differential geometric study of the manifold of probability models, where each probability distribution is just a point on the manifold. Instead of using metric for measuring distances on such manifolds, these applications often use â€œdivergence functionsâ€ for measuring proximity of two points (that do not impose symmetry and triangular inequality), for instance Kullback-Leibler divergence, Bregman divergence, f-divergence, etc. Divergence functions are tied to generalized entropy (for instance, Tsallis entropy, Renyi entropy, phi-entropy) and cross-entropy functions widely used in machine learning and information sciences. After a brief introduction to IG, I illustrate the geometry of maximum entropy inference and exponential family. I then use a general form of entropy/cross-entropy/divergence function, and show how the geometry of the underlying probability manifold (deformed exponential family) reveals an â€œescort statisticsâ€ that is hidden from the standard exponential family. Speaker(s): Jun Zhang (University of Michigan)

]]>Speaker(s): Kyler Siegel (Columbia University)

]]>Speaker(s): Christopher Ryba (MIT)

]]>I have been fascinated how even innocent symmetry forces many systems to be classifiable, and satisfy other unexpected properties. Case in point are commuting expanding maps of compact manifolds. Either they have common powers or they arise by taking products or are smoothly equivalent to a linear expanding on a torus or nilmanifold. The extra symmetry here refers one map commuting with anther nontrivially.

I will explain underlying ideas, some results and applications. Speaker(s): Ralf Spatzier (Michigan)

https://arxiv.org/abs/1906.11816 Speaker(s): Sanal Shivaprasad (UM)

]]>Speaker(s): Jonathan Gerhard

]]>Speaker(s): Yuping Ruan (UM)

]]>Speaker(s): Wei Ho (University of Michigan)

]]>Speaker(s): Jeremy Miller (Purdue University)

]]>Speaker(s): Jeremy Miller (Purdue University)

]]>Speaker(s): Tomas Berggren (KTH, Stockholm)

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

]]>Speaker(s): Carl Wang-Erickson (University of Pittsburgh)

]]>Speaker(s): Anthony Della Pella (University of Michigan)

]]>Following lecture 10 from http://www.math.harvard.edu/~lurie/252x.html. Speaker(s): Yunze Lu (UM)

]]> In 2017, the sphere packing problem in dimension 8 and 24 was solved. The Leech lattice gives the optimal solution in dimension 24. Since the other dimensions except 1,2,3 are open, the Leech lattice is especially interesting. In this talk I would like to give an application of the theory of Leech lattice to Algebraic Geometry.

I will discuss the automorphism groups of Kummer and Enriques surfaces, and some recent progress. Speaker(s): Shigeyuki Kondo (Nagoya University)

Speaker(s): Karthik Ganapathy (University of Michigan Ann Arbor)

]]>Speaker(s): Feng Zhu (UM)

]]>The 19th century idea of ``Durfee squaresâ€™â€™ produced an effective combinatorial trick to count partitions. (In fact, one of its modern incarnations is the h-index measuring mathematiciansâ€™ productivity.) The resulting identity has been reinterpreted in Donaldson-Thomas theory as the comparison of two ways of calculating DT invariants of the A2 quiver. In this talk, we will explore the DT quantum dilogarithm identities and their infinite-variable generalizations via motivic characteristic classes. No prior knowledge is assumed about any of the mentioned areas. Speaker(s): Richard Rimanyi (University of North Carolina)

]]>Speaker(s): Jack Carlisle (University of Michigan)

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

]]>Assigning characteristic classes to singular varieties is an effective way of studying the enumerative properties of the singularities. Initially one wants to consider the so-called fundamental class in H, K, or Ell, but it turns out that in Ell such a class is not well defined. However, a deformation of the notion of fundamental class (under the name of Chern-Schwartz-MacPherson class in H, motivic Chern class in K) extends to Ell, due to Borisov-Libgober. To make sense of the Borisov-Libgober class for a wider class of singularities we introduce a version of it, which now necessarily depends on new (`dynamicalâ€™ or `Kahlerâ€™) variables. We obtain that this elliptic class of Schubert varieties satisfies two different recursions (Bott-Samelson, and R-matrix recursions). The second one relates elliptic Schubert calculus with Felder-Tarasov-Varchenko weight functions, and Aganagic-Okounkov stable envelopes. The duality between the two recursions is an incarnation of 3d mirror symmetry (and symplectic duality). Joint work with A. Weber. Speaker(s): Richard Rimanyi (University of North Carolina)

]]>Speaker(s): Clark Butler (IAS)

]]>Speaker(s): Michael Perlman (University of Notre Dame)

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

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

]]>Speaker(s): Olivier Lafitte (Paris 13)

]]>Speaker(s): Martin Bobb (U Texas)

]]>Consider a pressureless gas interacting through an attractive-repulsive potential given as a difference of power laws and normalized so that its unique minimum occurs at unit separation. For a range of exponents corresponding to mild repulsion and strong attraction, we show that the minimum energy configuration of gas is uniquely attained â€” apart from translations and rotations â€” by equidistributing the particles of gas over the vertices of a regular top-dimensional simplex (i.e. an equilateral triangle in two dimensions and regular tetrahedron in three).

If the attraction is not assumed to be strong, we show these configurations are at least local energy minimizers in the relevant d-infinity metric from optimal transportation, as are all of the other uncountably many unbalanced configurations with the same support. We infer the existence of phase transitions.

An ingredient in the proof which may have independent interest is the establishment of a simple isodiametric variance bound which generalizes Popoviciuâ€™s inequality from one to higher dimensions and characterizes regular simplices: it shows that among probability measures on R^n whose supports have at most unit diameter, the variance around the mean is maximized precisely by those measures which assign mass 1/(n + 1) to each vertex of a (unit-diameter) regular simplex.

Based on preprint with Tongseok Lim at https://arxiv.org/abs/1907.13593 Speaker(s): Robert McCann (University of Toronto)

The Lucas sequence is a sequence of polynomials in s and t defined recursively by {0}=0, {1}=1, and {n}=s{n-1}+t{n-2} for n greater than 1. On specialization of s and t one can recover the Fibonacci numbers, the nonnegative integers, and the q-integers [n]_q. Given a quantity which is expressed in terms of products and quotients of positive integers, one obtains a Lucas analogue by replacing each factor of n in the expression with {n}. It is then natural to ask if the resulting rational function is actually a polynomial in s and t and, if so, what it counts. Using lattice paths, we give a combinatorial model for the Lucas analogue of binomial coefficients.

This is joint work with Curtis Bennett, Juan Carrillo, and John Machacek. We then give an algebraic mehod for proving polynomiality using a connection with cyclotomic polynomials via gamma expansions. This part of the talk is joint work with Jordan Tirrell and based on an idea of Richard Stanley. Finally we, also consider Catalan numbers and their relatives, such as those for finite Coxeter groups.

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

Two Six Labs (https://www.twosixlabs.com/) is a technology company based out of Arlington, VA, but with remote offices all over the country. Our research team has expertise in cyber-security, data science and mobile security. I'll talk about my transition from academia to industry, how I found myself in cyber security, and about opportunities at Two Six. I'll talk about some of the projects I've worked on, and how my background in Mathematics intersects with my current work. We'll finish up with some fun exploits I discovered over the past year, such as causing denial of service with a PDF file, filling up the disk of a VNC server (without needing login credentials), and taking down popular websites from their user signup page.

About David: David Renardy is a Lead Research Scientist at Two Six Labs. He got his PhD in Mathematics from the University of Michigan in 2016 under the direction of Dick Canary.

Reception to Follow.

There will be an exclusive event for PhD students in our Invitations to Industry series through the Erdos Institute featuring David Renardy (UM Math PhD 2016, now Senior Research Scientist at Two Six Lab). This is in addition to the career fair earlier in the afternoon. Speaker(s): David Renardy (Two Six Labs)

http://front.math.ucdavis.edu/1906.07106 Speaker(s): Rachel Webb (UM)

]]>Speaker(s): Mitul Islam (UM)

]]>Speaker(s): Karol Koziol (University of Michigan)

]]>Speaker(s): Antonio Auffinger (Northwestern University)

]]>Speaker(s): Sridhar Venkatesh (UM)

]]>Speaker(s): Brian Hwang (Cornell University)

]]>Following lectures 11-13 from http://www.math.harvard.edu/~lurie/252x.html. Speaker(s): Attilio Castano (UM)

]]>Speaker(s): Yueqiao Wu (UM)

]]>Speaker(s): Benoit Pausader (Brown University)

]]>Speaker(s): Yunze Lu (University of Michigan)

]]>Speaker(s): Patrick Kelly (UM)

]]>Speaker(s): Junliang Shen (MIT)

]]>We introduce a general framework for continuous-time betting markets, in which a bookmaker can dynamically control the prices of bets on outcomes of random events. In turn, the prices set by the bookmaker affect the rate or intensity of bets placed by gamblers. The bookmaker seeks a price process that maximizes his expected (utility of) terminal wealth. We obtain explicit solutions or characterizations to the bookmakerâ€™s optimal bookmaking problem in various interesting models.

Joint work with Matthew Lorig and Zhou Zhou. Speaker(s): Bin Zou (University of Connecticut)

Speaker(s): Ben Dozier (Stony Brook)

]]>Speaker(s): Ben Dozier (Stony Brook)

]]>TBA Speaker(s): Karen Smith (University of Michigan)

]]>Speaker(s): Beatrice Bonga (Perimeter Institute for Theoretical Physics, Waterloo, Canada)

]]>Speaker(s): Bogdan Zavyalov (Stanford/UM)

]]>Speaker(s): Doug Wright (Drexel University)

]]>Given a nested decreasing family of targets B_n in a measure space X equipped with a flow phi_t (or transformation), the shrinking target problem asks to characterize when there is a full measure set of points x that hit the targets infinitely often in the sense that {n \in N : phi_n(x)\in B_n} is unbounded. This talk will examine the discrete shrinking target problem for the TeichmÃ¼ller flow on the moduli space of unit-area quadratic differentials and show that for any ergodic probability measure, almost every differential will hit a nested spherical targets infinitely often provided the measures of the targets are not summable. Our key tool is an effective mean ergodic theorem stating that the time-average of any L^2 function converges to its space-average at a uniform rate in L^2. As an application, we obtain a logarithm law describing how quickly generic discrete geodesic trajectories accumulate on a given point. Joint with Grace Work. Speaker(s): Spencer Dowdall (Vanderbilt University)

]]>I will present some basic concepts and tools of the theory of stochastic processes, starting from discrete-time (stochastic) control theory and game theory. Also, I will present the main open problem in discrete-time stochastic games: whether every stochastic game with finitely many players (N>2), states, and actions, has a uniform equilibrium payoff.

Then I will motivate the continuous-time models making the connection between stochastic control and games with partial differential equations. I will end the talk with a presentation of asymptotic analysis of many-player games using the concept of mean-field games introduced by Pierre-Louis Lions and Jean-Michel Lasry (2006). Speaker(s): Asaf Cohen (Michigan)

http://front.math.ucdavis.edu/1902.05745 Speaker(s): Jakub Witaszek (UM)

]]>Speaker(s): Harry Richman

]]>Speaker(s): Samantha Pinella (UM)

]]>Speaker(s): Tasho Kaletha (University of Michigan)

]]>Speaker(s): Nicholas McCleerey (Northwestern University)

]]>Speaker(s): Karl Liechty (DePaul University)

]]>Speaker(s): Swaraj Pande (UM)

]]>TBA

]]>Speaker(s): Berkan Yilmaz (University of Michigan)

]]>Following lectures 14-16 from http://www.math.harvard.edu/~lurie/252x.html. Speaker(s): Shubhodip Mondal (UM)

]]>Speaker(s): Lukas Scheiwiller (University of Michigan Ann Arbor)

]]>Speaker(s): Sayantan Khan (UM)

]]>In many situations our best mathematical models for fluid flows are the Navier-Stokes and the Euler equations. In this talk we will focus on incompressible flows. We will discuss some of the open questions concerning the equations in parallel with similar questions for simpler models for which it is possible to make a more complete analysis. Speaker(s): Vladimir Sverak (University of Minnesota)

]]>Speaker(s): Yunze Lu (University of Michigan)

]]>Speaker(s): Bogdan Zavyalog (Stanford University)

]]>Speaker(s): Ilya Khayutin (Northwestern)

]]>Speaker(s): Ilya Khayutin (Northwestern)

]]>Speaker(s): Serin Hong (UM)

]]>Speaker(s): Alex Hening (Tufts University)

]]>Speaker(s): Helen Jenne (University of Oregon)

]]>Algebraic cycles on varieties over number fields behave very differently than over the complex numbers. I will explain some of the differences, and discuss some of the open problems in the area. Speaker(s): Kartik Prasanna (Michigan)

]]>Speaker(s): DÃdac MartÃnez-Granado (Indiana University)

]]>https://arxiv.org/abs/1707.05121 Speaker(s): Shizhang Li (UM)

]]>Speaker(s): Gilyoung Cheong

]]>Speaker(s): Salman Siddiqi (UM)

]]>Speaker(s): Bhargav Bhatt (University of Michigan)

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

]]>Speaker(s): Wanlin Li (MIT)

]]>Speaker(s): Elizabeth Collins-Wildman (University of Michigan)

]]>Following lectures 17-18 from http://www.math.harvard.edu/~lurie/252x.html. Speaker(s): Ruian Chen (UM)

]]>Details about the Learning Community may be found at

http://www.math.lsa.umich.edu/~glarose/dept/teaching/lcit.html . Speaker(s): LCIT Discussion

Speaker(s): Carsten Peterson (UM)

]]>Speaker(s): Andrew Snowden (University of Michigan)

]]>Speaker(s): Mike Zieve (U(M))

]]>Speaker(s): Konstantinos Tsouvalas (UM)

]]>Speaker(s): Shelby Cox

]]>Speaker(s): Shizhang Li (University of Michigan)

]]>Speaker(s): Lukas Scheiwiller (UM)

]]>Speaker(s): Yuan Liu (University of Michigan)

]]>Following lectures 19 and 20 from http://www.math.harvard.edu/~lurie/252x.html. Speaker(s): Attilio Castano (UM)

]]>Speaker(s): Alapan Mukhopadhyay (University of Michigan Ann Arbor)

]]>Speaker(s): Salman Siddiqi (UM)

]]>Speaker(s): TBA

]]>Speaker(s): Attilio Castano (University of Michigan)

]]>Speaker(s): Ani Agarwal (UM)

]]>Speaker(s): Benjamin Bakker (University of Georgia)

]]>Speaker(s): Nicolas Tholozan (ENS)

]]>Speaker(s): Nicolas Tholozan (ENS)

]]>Speaker(s): Juliette Bruce (University of Wisconsin-Madison)

]]>Speaker(s): Andrew Snowden (UM)

]]>Speaker(s): Erdos Institute (Invitations to Industry series)

]]>Speaker(s): Anna Vainchtein (University of Pittsburgh)

]]>Speaker(s): Nicolas Tholozan (ENS)

]]>

Machine learning has promised a new way to gain understanding and value in many industries; yet most companies are still learning how to correctly use and design ML models. The main obstacles come from many different sources, which include the inherent complexity of ML models, extracting economic value from data, deployment, integration, legacy models and innovation. At layer 6 we approach these problems from a different perspective: by engaging in research we are able to produce high impact papers as well as keep ourselves updated with the state-of-the-art approaches, by doing competitions we tune our skills into the challenges of real world data, and by working in use-cases we deal with the complexities of a large organization. In this talk I will share what is to work in this environment as well as what are the main skills that are needed to work in the ML industry.

Felipe Perez, UM Math PhD 2015, is now a Machine Learning Research Scientist at Layer 6 AI. Our Invitation to Industry Series is run in collaboration with the Erdos Institute.

Speaker(s): Felipe Perez (Layer 6 AI)

https://arxiv.org/abs/1907.08670 Speaker(s): Haoyang Guo (UM)

]]>Speaker(s): Karthik Ganapathy

]]>Speaker(s): Carsten Peterson (UM)

]]>Speaker(s): Yuan Liu (University of Michigan)

]]>Speaker(s): Jiaoyang Huang (Institute for Advanced Study)

]]>Speaker(s): Andy (UM)

]]>Speaker(s): Ananth Raghuram (IISER, Pune)

]]>Following lectures 21 and 22 from http://www.math.harvard.edu/~lurie/252x.html. Speaker(s): Emanuel Reinecke (UM)

]]>Speaker(s): AndrÃ©s ServellÃ³n (University of Michigan Ann Arbor)

]]>Speaker(s): Yuping Ruan (UM)

]]>Speaker(s): Shuichiro Takeda (University of Missouri)

]]>I will present two models of optimal consumption under a constraint that prevents the agent's consumption to fall below a certain proportion of her current "consumption habit." In the first model, consumption habit is the running maximum of past consumption, while the second model assumes that habit is the exponentially weighted moving average of past consumption. For each case, a stochastic control problem is formulated with the objective of maximizing the expected discounted utility of consumption stream while investing in a Black-Scholes financial market. The resulting Hamilton-Jacobi-Bellman equations are reduced to non-linear free-boundary problems that are subsequently solved semi-explicitly. The optimal consumption policy in the two models share common features in that they are mainly driven by the wealth-to-habit ratio. Furthermore, there are critical values of the wealth-to-habit ratio that determines when it is optimal to consume at the minimum acceptable rate, when should the consumption rate be above the minimum, and when is it optimal to raise the consumption habit above its current value.

The talk is based on joint work with Erhan Bayraktar and Virginia Young. Speaker(s): Bahman Angoshtari (University of Washington)

Speaker(s): Jia Zhi (Andy) Jiang (University of Michigan)

]]>Speaker(s): Yusuke Nakamura (University of Tokyo)

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

]]>http://front.math.ucdavis.edu/1810.00049 Speaker(s): Alapan Mukhopadhyay (UM)

]]>following "Formal group laws arising from Algebraic varieties" by Artin-Mazur. Speaker(s): Haoyang Guo (UM)

]]>We consider weakly interacting jump processes on time-varying random graphs with dynamically changing multi-color edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution of all other nodes and the corresponding edges, while the edge dynamics depends on the corresponding nodes. Asymptotic results, including law of large numbers, propagation of chaos, and central limit theorems, are established. In contrast to the classic McKean-Vlasov limit, the limiting system exhibits a path-dependent feature in that the evolution of a given particle depends on its own conditional distribution given its past trajectory. We also analyze the asymptotic behavior of the system when the edge dynamics is accelerated. A law of large number and a propagation of chaos result is established, and the limiting system is given as independent McKean-Vlasov processes. Errors between the two limiting systems, with and without acceleration in edge dynamics, are also analyzed.

Joint work with Erhan Bayraktar Speaker(s): Ruoyu Wu (UM)

Speaker(s): reserved

]]>Given an equity market with n stocks, a pseudo-arbitrage is an investment strategy (i.e. a portfolio map) which outperforms the market portfolio (i.e. the buy-and-hold option) almost surely in the long run. When the market weights evolve via some unknown discrete time process, Fernholz proved that such portfolio maps exist, under mild and realistic assumptions. Recently, Pal and Wong showed that the problem of finding pseudo-arbitrages is equivalent to solving a certain Monge-Kantorovich optimal transport problem where the cost function is given by the so-called "diversification return," which is closely related to the free energy in statistical physics. In our work, we study the regularity theory for these maps. In other words, we consider the question "If the market conditions change slightly, does the investment portfolio also change in a continuous way?" By addressing this problem, an unexpected connection to KÃ¤hler geometry emerges. This provides a new geometric interpretation for the regularity theory of optimal transport. Speaker(s): Gabriel Khan (UM)

]]>Why it appears to be much harder to compute the permanent than the determinant of a (complex) matrix?

Essentially, this is one of the seven â€œmillion dollarsâ€ millennium problems, and, arguably, the one that we understand the least. I plan to discuss what kind of mathematics we can possibly use to answer this and similar questions. An attractive feature of the computational complexity questions is that a) they sound elementary and b) virtually anything (algebra, geometry/topology, analysis, none of the above)

can be a key to the answer. In particular, I plan to discuss some recent connections to complex analysis and statistical physics. Speaker(s): Alexander Barvinok (Michigan)

Speaker(s): Christian Schnell (Stony Brook University)

]]>Speaker(s): Brian Lawrence (Chicago)

]]>We study the problem of minimizing the discounted probability of exponential Parisian ruin, that is, the discounted probability that an insurerâ€™s surplus exhibits an excursion below zero in excess of an exponentially distributed clock. The insurer controls its surplus via reinsurance priced according to the mean-variance premium principle, as in Liang, Liang, and Young [23]. We consider the classical risk model and apply stochastic Perronâ€™s method, as introduced by Bayraktar and Sirbu [9, 10, 11], to show that the minimum discounted probability of exponential Parisian ruin is the unique viscosity solution of its Hamilton-Jacobi-Bellman equation with boundary conditions at infinity. A major difficulty in proving the comparison principle arises from the discontinuity of the Hamiltonian.

Speaker(s): Xiaoqing Liang (Visiting Scholar at UM)

Speaker(s): Jaekyoung Kim (KAIST)

]]>I will discuss a classic inverse spectral problem for a Sturm Liouville differential operator in a bounded interval. The goal is to understand how one can approach this problem in a discrete setting, using finite differences and a computationally efficient inversion algorithm, which can then be extended to inverse wave scattering problems in a cavity.

Speaker(s): Liliana Borcea (Michigan)

Speaker(s): reserved

]]>Speaker(s): CRLT

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

]]>Speaker(s): Nir Gadish (MIT)

]]>Speaker(s): Olivia Walch (CEO at Arcascope)

]]>Speaker(s): Myrto Mavraki (Northwestern/University of Basel)

]]>Speaker(s): Alexandra Florea (Columbia University)

]]>Speaker(s): Konstantin Tikhomirov (Georgia Tech)

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]]>Speaker(s): Diogo Gomes (KAUST)

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]]>Speaker(s): Laura DeMarco (Northwestern University)

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

]]>Speaker(s): Osman Basaran (Purdue University)

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]]>Speaker(s): Karen Parshall (University of Virginia)

]]>Speaker(s): Leo Neufcort (MSU)

]]>Speaker(s): Dmitry Chelkak (Steklov Mathematical Institute and ENS)

]]>Speaker(s): Sarah Olson (Worcester Polytechnic Institute)

]]>In this very popular event, we bring back UM Math PhD alumni who are working in industry to discuss their careers and paths in a panel format. This year, in celebration of the data revolution which has generated the current hunger for PhD level mathematicians in non-academic spaces, our panelists are all recent PhDs from our department working in various industries and positions related to DATA.

Tentative Panelists are Ross Kravitz (Data Scientist at Stripe), Hunter Brooks (Principal Data Scientist at Oracle Data Cloud (Moat)), Becky Hoai (data consultant at Slalom), Alex Mueller (Founder and CEO, Capnion). Speaker(s): UM PhD Alumni (various)

Speaker(s): Winter Break

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]]>Speaker(s): Laure Saint Raymond (ENS, Lyons)

]]>In this talk, I will discuss rank-dependent diffusions. I will focus on two models: Up the River model and N-player games with fuel constraints. These problems require treating carefully the corresponding PDEs. The former is joint with Li-Cheng Tsai, and the latter joint with Xin Guo and Renyuan Xu. Speaker(s): Wenpin Tang (UCLA)

]]>Speaker(s): Bangere Purnaprajna (University of Kansas)

]]>Speaker(s): Laure Saint Raymond (ENS Lyon, France)

]]>Speaker(s): Demetrios Papageorgiou (Imperial College, London)

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]]>Speaker(s): Bruno Klingler (Humboldt University)

]]>Speaker(s): Bruno Klingler (Humboldt University)

]]>The goal of scientific computing is to simulate a scientific process when it is too difficult to study by experiment or theory. A scientific computing project requires (1) a mathematical model or set of equations describing the problem, (2) an algorithm for solving the equations, and (3) a computer program to implement the algorithm. Scientific computing research is carried out in academia, industry, and the national labs. There is continuing need to improve the accuracy and efficiency of the simulations, and to extend their scope to challenging new problems. This talk will give an overview of scientific computing and discuss some examples from my work in fluid dynamics and protein/solvent electrostatics. Speaker(s): Robert Krasny (Michigan)

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]]>Speaker(s): David Fisher (Indiana University)

]]>Speaker(s): Rob Littleton (Cover My Meds)

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]]>Speaker(s): CRLT CRLT (University of Michigan)

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

]]>Speaker(s): John Voight (Dartmouth College)

]]>Speaker(s): John Voight (Dartmouth College)

]]>TBA

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

]]>Speaker(s): Erdos Institute

]]>Speaker(s): Hang Xue (University of Arizona)

]]>Speaker(s): Akshay Venkatesh (IAS, Princeton)

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