Work of Levasseur and Stafford describes the rings of differential operators on various classical invariant rings of characteristic zero; in each of these cases, the differential operators form a simple ring. Towards an attack on the simplicity of rings of differential operators on invariant rings of reductive groups over the complex numbers, Smith and Van den Bergh asked if reduction modulo p works for differential operators in this context. In joint work with Jack Jeffries, we establish that this is not the case for various classical groups. Speaker(s): Anurag Singh (University of Utah)

]]>I will give an example of an open 3-manifold M that is locally hyperbolic, its fundamental group has no divisible subgroup, but M is not hyperbolic. This example answers a question of Agol. Moreover, I will use it to illustrate a result on hyperbolization for a particular class of open 3-manifolds with infinitely generated fundamental group Speaker(s): Tommaso Cremaschi (University of Southern California)

]]>We will discuss some mathematical questions in mathematical wave turbulence, focusing on the rigorous understanding of the so-called wave kinetic equation. Speaker(s): Zaher Hani (Michigan)

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

]]>Motivated by applications such as ink jet printing, drop-by-drop manufacturing, sprays, emulsions, and chemical separations, we study the dynamics of breakup and coalescence through high-accuracy simulation, theory, and experiment. In this talk, I will highlight our group's work on accurately capturing the fluid dynamics that takes place in the vicinity of finite-time singularities. The free surface flow algorithms and solvers that we develop and use rely on a sharp interface representation of phase boundaries. In the simulations, we are able to analyze situations that involve disparate length scales that differ by up to seven orders of magnitude (commercial codes can handle about 2-3 orders and custom codes can capture at most 3-4 orders of magnitude disparity in length scales). The primary focus of the talk will be on simulations of the breakup of surfactant covered filaments where I will pay special attention to the pinch-off singularity. I will also summarize some of our recent work on the pre- and post-coalescence singularities that arise when two drops or bubbles are driven together and made to merge into one. Speaker(s): Osman Basaran (Purdue University)

]]>Let $G$ be a Kac-Peterson group associated to a symmetrizable generalized Cartan matrix. Let $(b, d)$ be a pair of positive braids associated to the root system. We define the double Bott-Samelson cell associated to G and (b,d) to be the moduli space of configurations of flags satisfying certain relative position conditions. We prove that they are affine varieties and their coordinate rings are upper cluster algebras. We construct the Donaldson-Thomas transformation on double Bott-Samelson cells and show that it is a cluster transformation. In the cases where G is semisimple and the positive braid (b,d) satisfies a certain condition, we prove a periodicity result of the Donaldson-Thomas transformation, and as an application of our periodicity result, we obtain a new geometric proof of Zamolodchikov's periodicity conjecture in the cases of (D, A_r). In the cases where G is of Dynkin type A_r, we prove that the undecorated double Bott-Samelson cell is an Legendrian invariant associated to the closure of the pair of positive braids (b,d). This is joint work with Linhui Shen. Speaker(s): Daping Weng (Michigan State University)

]]>Speaker(s): Monica Lewis (University of Michigan)

]]>Abstract: Motivated by applications such as ink jet printing, drop-by-drop manufacturing, sprays, emulsions, and chemical separations, we study the dynamics of breakup and coalescence through high-accuracy simulation, theory, and experiment. In this talk, I will highlight our group’s work on accurately capturing the fluid dynamics that takes place in the vicinity of finite-time singularities. The free surface flow algorithms and solvers that we develop and use rely on a sharp interface representation of phase boundaries. In the simulations, we are able to analyze situations that involve disparate length scales that differ by up to seven orders of magnitude (commercial codes can handle about 2-3 orders and custom codes can capture at most 3-4 orders of magnitude disparity in length scales). The primary focus of the talk will be on simulations of the breakup of surfactant-covered filaments where I will pay special attention to the pinch-off singularity. I will also summarize some of our recent work on the pre- and post-coalescence singularities that arise when two drops or bubbles are driven together and made to merge into one.

Bio: Motivated by applications in ink jet printing, separations, production of emulsions, dispersions, and double-emulsions, and drop-wise manufacturing, Prof. Basaran’s research involves the use of a balanced approach based on computation, theory, and experiment to attack a number of fundamental issues that lie at the heart of such practical problems. Currently, the research is organized along the following key themes.

Speaker(s): Devlin Mallory (UM)

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

]]>Speaker(s): Scott Neville

]]>We present explicit finite size results on the mean quantum pu-

rity and von Neumann entropy over the Bures-Hall measure. A key

ingredient of the calculations is the recently discovered connection be-

tween the correlation functions of Bures-Hall ensemble and these of

the Cauchy-Laguerre biorthogonal ensemble. (This talk is based on

the preprint arXiv:2002.04085.) Speaker(s): Lu Wei (University of Michigan)

I will discuss a theory of endoscopy for certain symmetric spaces associated to unitary groups, the main result being the fundamental lemma for the "Lie algebra". This is motivated by the study of certain periods of automorphic forms on unitary groups with applications to arithmetic. After explaining where the fundamental lemma fits into this broader picture, I will describe its proof if time permits. Speaker(s): Spencer Leslie (Duke University)

]]>Speaker(s): Christopher Stith (University of Michigan)

]]>Speaker(s): Konstantinos Tsouvalas

]]>World War I had marked a break in business as usual within the American mathematical research community. In its aftermath, there was a strong sense of entering into “a new era in the development of our science.” And then the stock market crashed. Would it be possible in such newly straitened times to sustain into the 1930s the momentum that American mathematicians had managed to build in the 1920s? This talk will explore the contours of an answer to that question. Speaker(s): Karen Parshall (University of Virginia)

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

]]>In this joint work with Philip Protter we consider a general market with a semimartingale asset price and study the situation where an ``insider'' agent has access to a continuous flow of additional information generated by a stochastic process. Assuming no arbitrage conditions, the price process remains a semimartingale for the expanded filtration; it is then characterized by an (additional) information drift. The information drift is a key proxy to the statistical advantage provided by the additional information. The core of our results consists in a series of convergence theorems for semimartingale decompositions based on $L^p$ norms, which provides a representation of the information drift for continuous expansions. These tools are employed to study a new class of models for the information accessible to high-frequency traders.

Speaker(s): Leo Neufcort (MSU)

Mirror symmetry is a fast-moving research area at the boundary between mathematics and theoretical physics. Originated from observations in string theory, it suggests that complex Calabi-Yau manifolds should come in mirror pairs, in the sense that geometrical information of a Calabi-Yau manifold can be read through invariants of its mirror.

In the first part of the talk, I will introduce some geometrical ideas inspired by mirror symmetry. In particular, I will go through the main steps which relate mirror symmetry to non-archimedean geometry and the theory of Berkovich spaces.

In the second part, I will describe a combinatorial object which emerges in mirror symmetry and in birational geometry, the so-called dual complex of degeneration of varieties. I will show how the techniques of Berkovich geometry give a new insight into the study of dual complexes. In a joint work with Morgan Brown, we determine the homeomorphism type of the dual complex of some degenerations of hyper-Kaehler manifolds. The results are in accordance with the predictions of mirror symmetry, and the recent work about the rational homology of dual complexes of degenerations of hyper-Kaehler varieties, due to Kollar, Laza, Sacca and Voisin. Speaker(s): Enrica Mazzon (Max Planck Institute)

Anosov flows are central objects in dynamics, generalizing the basic example of a geodesic flow over a Riemann surface.

In the talk we will introduce those flows and their dynamical behavior.

Moreover, we show how the factorization method, pioneered by Eskin and Mirzakhani in their groundbreaking work about measure rigidity for the moduli space of translation surfaces, can be adapted to smooth ergodic theory and in particular towards the study of Anosov flows.

Using this adaption, we show that for a quantitatively non-integrable Anosov flow, every generalized u-Gibbs measure is absolutely continuous with respect to the whole unstable manifold.

In the talk I will introduce the concept, the relations to previous works (Eskin-Mirzakhani, Eskin-Lindenstrauss) and the result with some applications. Technical details will be given on the Thursday seminar.

Speaker(s): Asaf Katz (U Chicago)

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

]]>The factorization method is a technical method, which allows one to choose generic points satisfying the constraints needed for the Eskin-Mirzakhani technique, overcoming some difficulties arising in the settings of smooth dynamics world compared to homogeneous dynamics. In the lecture, I will introduce the factorization theorem and ideas in its proof.

Moreover I will discuss how one can combine this technique together with the usage of normal forms coordinates, developed by Katok and Kalinin-Sadovskaya, in order to deduce measure rigidity results in smooth dynamics. Speaker(s): Asaf Katz (University of Chicago)

Blickle, Mustata and Smith proposed two conjectures on the limits of F-pure thresholds. One conjecture asks whether or not the limit of a sequence of F-pure thresholds of principal ideals on regular local rings of fixed dimension can be written as an F-pure threshold in lower dimension. Another conjecture predicts that any F-pure threshold of a formal power series can be written as the F-pure threshold of a polynomial. In this talk, we prove that the first conjecture has a counterexample but a weaker statement still holds.

We also give a partial affirmative answer to the second conjecture. Speaker(s): Kenta Sato (iTHMS, Riken)

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

]]>Microorganisms can swim in a variety of environments, interacting with chemicals and other proteins in the fluid. In this talk, we will highlight recent computational methods and results for swimming efficiency and hydrodynamic interactions of swimmers in different fluid environments. Sperm are modeled via a centerline representation where forces are solved for using elastic rod theory. The method of regularized Stokeslets is used to solve the fluid-structure interaction where emergent swimming speeds can be compared to asymptotic analysis. In the case of fluids with extra proteins or cells that may act as friction, swimming speeds may be enhanced and attraction may not occur. Speaker(s): Sarah Olson (Worcester Polytechnic Institute)

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

]]>Abstract: Microorganisms can swim in a variety of environments, interacting with chemicals and other proteins in the fluid. In this talk, we will highlight recent computational methods and results for swimming efficiency and hydrodynamic interactions of swimmers in different fluid environments. Sperm are modeled via a centerline representation where forces are solved for using elastic rod theory. The method of regularized Stokeslets is used to solve the fluid-structure interaction where emergent swimming speeds can be compared to asymptotic analysis. In the case of fluids with extra proteins or cells that may act as friction, swimming speeds may be enhanced and attraction may not occur.

Bio: Sarah Olson is an Associate Professor in the Department of Mathematical Sciences at Worcester Polytechnic Institute. Olson received her undergraduate degrees in Mathematics and Biology from Providence College, a master’s from the University of Rhode Island in Mathematics, and a PhD in Biomathematics from North Carolina State University. She has worked in the general areas of fluid dynamics, scientific computing, and mathematical biology.

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): Yueqiao Wu (UM)

]]>Speaker(s): Winter Break

]]>Speaker(s): Shelby Cox

]]>Speaker(s): Harini Desiraju (SISSA, Trieste)

]]>Speaker(s): Wayne Raskind (Wayne State University)

]]>Speaker(s): Zhenghui Huo (University of Toledo)

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

]]>Speaker(s): Sayantan Khan

]]>Speaker(s): Kyu Jun (University of Michigan)

]]>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): Marcus Robinson (University of Utah)

]]>Stratification of the density in an incompressible fluid is responsible for the propagation of

internal waves. In domains with topography, the interaction of these waves with the boundary

produces a cascade towards small wavelengths. Although the equations are linear, this phenomenology is reminiscent from

turbulence. Speaker(s): Laure Saint Raymond (ENS, Lyons)

Speaker(s): Reebhu Bhattacharyya (University of Michigan)

]]>Multilayer flows such as falling films and coating flows, or pressure-driven

flows of immiscible fluids in channels and pipes, are fundamental in applications.

Such flows are typically stable if they are slow enough (highly viscous). Such regimes arise in small-scale geometries (e.g. microfluidics), and electric fields can be used to drive the system out of equilibrium to produce patterning, mixing and phase separation.

I will begin with some experiments and direct numerical simulations (DNS) that show how electric fields can be utilized in their dual role of inducing instabilities or stability depending on geometry and orientation. I will then review the theoretical models underpinning such phenomena and will use asymptotic theories to derive and study reduced-dimension model equations that describe nonlinear interfacial waves in the presence of fields. Computations predict rich dynamics including spatiotemporal chaos and singularity formation. Some novel inertialess nonlinear interfacial instabilities will also be described - these arise due to flux functions of derived evolution equations changing type from hyperbolic to elliptic. Finally, I will present results on the use of electric fields and/or blowing suction in achieving feedback and optimal control of falling film flows. Comparisons with DNS will be made and these will be used beyond the range of validity of asymptotic models to predict phenomena such as electrostatic suppression of Rayleigh-Taylor instabilities, and electrostatically induced pumping in microchannels. Speaker(s): Demetrios Papageorgiou (Imperial College, London)

The Grassmannian Gr(k,n) admits an action by a finite cyclic group of order n via the cyclic shift automorphism. The combinatorial structures underlying both total nonnegativity and clusters for Gr(k,n) are cyclically equivariant, which is one explanation for the particular elegance of these structures in the case of Gr(k,n). We will explore the L-shift locus in Gr(k,n), i.e. the subvariety of points fixed by the Lth power of the cyclic shift. Steven Karp recently showed that the 1-shift locus consists of finitely many points. On the other hand the n-shift locus is Gr(k,n) itself. Our theorems interpolate between these extremes: we provide a simple geometric description of the L-shift locus for any L, describe its total nonnegativity locus as a stratified space, and propose an atlas of generalized cluster charts (á la Chekhov-Shapiro) whose clusters are total positivity tests.

Speaker(s): Chris Fraser (University of Minnesota)

Speaker(s): Swaraj Pande (University of Michigan Ann Arbor)

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

]]>Speaker(s): Aidan Herderschee

]]>TBA

]]>Speaker(s): Malavika Mukundan (University of Michigan)

]]>Mehta and Ramanathan proved that globally F-split varieties (also called Frobenius split varieties) satisfy the Kodaira vanishing theorem. In this talk, I will show that a weak form of the Akizuki-Nakano vanishing theorem holds on globally F-split 3-folds. As its application, I will discuss the deformations of globally F-split Fano 3-folds. This is joint work with Kenta Sato.

Speaker(s): Shunsuke Takagi (University of Tokyo)

Speaker(s): Christopher Zhang

]]>Hodge theory, as developed by Deligne and Griffiths, is the main tool for analyzing the geometry and arithmetic of complex algebraic varieties. It is an essential fact that at heart, Hodge theory is NOT algebraic. On the other hand, according to both the Hodge conjecture and the Grothendieck period conjecture, this transcendence is severely constrained.

Tame geometry, whose idea was introduced by Grothendieck in the 80s, seems a natural setting for understanding these constraints. Tame geometry, developed by model theorists as o-minimal geometry, has for prototype real semi-algebraic geometry, but is much richer. It studies structures where every definable set has a finite geometric complexity.

The aim of these lectures is to present a number of recent applications of tame geometry to several problems related to Hodge theory and periods. Speaker(s): Bruno Klingler (Humboldt University)

Speaker(s): Yiwang Chen (University of Michigan)

]]>I will discuss how tame geometry can be used to prove algebraization results, either starting from diophantine informations (Pila-Wilkie theorem) or in a complex analytic setting (Chow and GAGA theorems in definable complex analytic geometry: results of Peterzil-Starchenko and Bakker-Brunebarbe-Tsimerman). Speaker(s): Bruno Klingler (Humboldt University)

]]>TBA Speaker(s): Florian Stecker (University of Texas - Austin)

]]>Speaker(s): Luis Nunez-Betancourt (Cimat)

]]>Speaker(s): Hao Jia (Univ. of Minnesota)

]]>I will sketch the proof that period maps associated to variations of pure Hodge structures on complex quasi-projective varieties are tame (a recent result of Bakker, Tsimerman and myself). As a corolloray (using also the results from lecture 2) one obtains a simpler proof of a famous result of Cattani-Deligne-Kaplan: the algebraicity of Hodge loci; as well as the algebraicity of images of period maps. Speaker(s): Bruno Klingler (Humboldt University)

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

]]>Speaker(s): John Harlim (Penn State)

]]>Speaker(s): Graham White (Indiana University, Bloomington)

]]>Speaker(s): Farrah Yhee (University of Michigan Ann Arbor)

]]>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)

]]>TBA

]]>Speaker(s): Dmitry Chelkak (École Normale Supérieure)

]]>Many problems concerning periods are related to numerical and functional transcendence questions. I will explain Ax-Schanuel type results from abelian varieties to variations of Hodge structures, proven using tame geometry; and their applications to atypical intersections problems (André-Oort conjecture, Zilber-Pink conjecture). Speaker(s): Bruno Klingler (Humboldt University)

]]>Speaker(s): Bradley Zykoski (UM)

]]>Speaker(s): Zhi Jiang

]]>Speaker(s): Sophie Morel (CNRS/ENS de Lyon.)

]]>Speaker(s): Shubhankhar Sahai

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

]]>Speaker(s): Gebhard Martin (University of Bonn)

]]>In this paper, we consider a system of multi-dimensional path-dependent hierarchical forward backward stochastic variational inequalities (FBSVI). Both the forward and backward equations have subdifferential operators which generalize the reflection and skew factors. The forward stochastic variational inequalities are multi-dimensional, path-dependent, and built up hierarchically in a general way, which fully covers the stochastic volatility model in financial mathematics, and its newly explored variants with unknown well-posedness. Existence and uniqueness of a strong solution to the FBSVI is proved and the stability of the perturbed FBSVI system with a small positive parameter is investigated by asymptotic analysis. We further answered those questions on the one-dimensional hierarchical FBSVI with H\"older continuous coefficients. Speaker(s): Patricia Ning (UM (Stat))

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

]]>Speaker(s): Linquan Ma (Purdue University)

]]>Speaker(s): Sophie Morel

]]>Let M1 and M2 be two Riemannian manifolds each of which have the boundary N. Consider the Laplacian on M1 and M2 augmented with Dirichlet boundary conditions on N. A natural question to ask is if there is any relation between spectral properties of the Laplacian on M1, M2, and the Laplacian on the manifold M (without boundary) obtained gluing together M1 and M2, namely M = M1 ∪N M2. Using spectral zeta functions, a partial answer is given by the Burghelea-Friedlander- Kappeler-gluing formula for zeta-determinants. This formula contains an (in general) unknown polynomial which is completely determined by some data on a collar neighborhood of the hypersurface N. I will use conformal transformations to understand the geometric content of this polynomial. The understanding obtained will pave the way for a fairly straightforward computation of the polynomial (at least for low dimensions of M). Furthermore it leads to a partial understanding of the heat invariant for the Dirichlet-to-Neumann map, that is for the Steklov problem. Speaker(s): Klaus Kristen (Mathematical Reviews AMS and Baylor University)

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

]]>Speaker(s): Julia Arciero (IUPUI)

]]>Speaker(s): Kyungyong Lee (University of Alabama)

]]>Speaker(s): Andrés Servellón (University of Michigan Ann Arbor)

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

]]>Speaker(s): Kevin Nowland and Benjamin Campbell (Cover My Meds)

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

]]>Speaker(s): Jonathan Gerhard

]]>TBA

]]>Speaker(s): Yuchen Liao (University of Michigan)

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

]]>Speaker(s): Yuping Ruan

]]>Speaker(s): Frank Sottile (Texas A&M)

]]>Speaker(s): Asaf Cohen (UM)

]]>Speaker(s): Federico Rodriguez Hertz

]]>Speaker(s): Justin Lyle (University of Kansas)

]]>TBA Speaker(s): Federico Rodriguez Hertz (Penn State)

]]>Speaker(s): Rishabh Gvalani (Imperial College, London)

]]>Speaker(s): Shubhankar Sahai (University of Michigan)

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

]]>Speaker(s): Joaquim Martins (University of Michigan)

]]>Speaker(s): Shelby Cox (University of Michigan Ann Arbor)

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

]]>Let S be a set and k a positive integer such that k is at most |S|. An action of a group G on S is called "k-transitive" if for every choice of distinct elements x_1, . . . , x_k of S and every choice of distinct targets y_1, . . . , y_k in S, there is an element g of G such that gx_i = y_i for each i = 1, . . . , k. The term "transitive" means 1-transitive, and actions with k > 1 are called "multiply transitive".

This talk is concerned with cusped hyperbolic 3-manifolds of finite volume whose group of isometries induces a multiply transitive action on the set of cusps of the manifold. Roger Vogeler conjectured that there is a largest k for which such k-transitive actions exist, and that for each k > 2, there is an upper bound on the possible number of cusps. Our proof of Vogeler’s conjecture will be discussed in this talk. Speaker(s): John Ratcliffe (Vanderbilt)

Speaker(s): Yuping Ruan (UM)

]]>Speaker(s): Harry Richman

]]>Speaker(s): Joshua Cape (University of Michigan)

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

]]>Speaker(s): Tejaswi Tripathi (University of Michigan)

]]>Speaker(s): Han Le (University of Michigan)

]]>Speaker(s): Karen Butt

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

]]>Speaker(s): Yifeng Huang (University of Michigan)

]]>Speaker(s): Mark De Cataldo (Stony Brook University)

]]>Speaker(s): Alexandros Saplaouras (UM)

]]>Speaker(s): Chandrika Sadanand (University of Illinois-Urbana Champaign)

]]>Speaker(s): Austyn Simpson (University of Illinois at Chicago)

]]>Speaker(s): Fabio Pusateri (University of Toronto)

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

]]>Speaker(s): Maria Cueto (Ohio State University)

]]>Speaker(s): TBA

]]>Speaker(s): Devlin Mallory (University of Michigan Ann Arbor)

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

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

]]>Speaker(s): Alana Huszar

]]>Speaker(s): Asad Lodhia (University of Michigan)

]]>Speaker(s): Cristian Popescu (UC San Diego)

]]>Speaker(s): Alex Ginsberg (University of Michigan)

]]>Speaker(s): Brian Chen (University of Michigan)

]]>Speaker(s): Konstantinos Tsouvalas

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

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

]]>Speaker(s): Devlin Mallory (University of Michigan)

]]>Speaker(s): Susan Friedlander (University of Southern California)

]]>Speaker(s): TBA

]]>Zhaoxu (Josh) Xi (2018 UM PhD, physics) Speaker(s): Zhaoxu (Josh) Xi (Upstart)

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

]]>Speaker(s): Jasmine Powell (UM)

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

]]>Speaker(s): Bradley Zykoski

]]>Speaker(s): Ruixiang Zhang (University of Wisconsin)

]]>We propose a mean field game model to study the question of how centralization of reward and computational power occur in the Bitcoin-like cryptocurrencies. Miners compete against each other for mining rewards by increasing their computational power. This leads to a novel mean field game of jump intensity control, which we solve explicitly for miners maximizing exponential utility, and handle numerically in the case of miners with power utilities. We show that the heterogeneity of their initial wealth distribution leads to greater imbalance of the reward distribution, or a "rich get richer" effect. This concentration phenomenon is aggravated by a higher bitcoin price, and reduced by competition. Additionally, an advanced miner with cost advantages such as access to cheaper electricity, contributes a significant amount of computational power in equilibrium. Hence, cost efficiency can also result in the type of centralization seen among miners of cryptocurrencies.

Speaker(s): Max Reppen (Princeton)

Speaker(s): Ricardo Grande (MIT)

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

]]>Speaker(s): John Lesieutre (Penn State University)

]]>Speaker(s): Huyen Pham (Universite Paris Diderot)

]]>Speaker(s): Huyen Pham (Universite Paris Diderot)

]]>Speaker(s): Huyen Pham (Universite Paris Diderot)

]]>