Speaker(s): Dominykas Norgilas (UM)

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

]]>Thin sheets folded into origami can create a rich variety of deployable, reconfigurable, and adaptable three-dimensional structures. The principles can be used in practical applications ranging from metamaterials and biomedical micro-robotics, to large-scale deployable architecture. This talk will present my groupâ€™s work in creating mechanics based numerical models for simulating and designing origami-inspired structures at multiple scales. The models are computationally efficient because they use a simplified bar and hinge framework to capture the geometry of the origami, yet they are capable of simulating kinematics, elastic deformations, multi-stability, stiffness properties, and contact in the structures. Capturing contact within the origami is especially important because contact can interfere with the folding kinematics, and can change the mechanical characteristics of the structures. Finally, the talk will present scenarios of how we apply these analytical tools. For example, simulating the self-assembly of micro-robots, evaluating the high stiffness-to-weight ratio in origami tubes, and capturing the complex stiffness anisotropy in origami with curved creases. Speaker(s): Evgueni Filipov (Civil and Environmental Engineering, UM)

]]>Speaker(s): Gilyong Cheung (University of Michigan)

]]>Speaker(s): Mikhail Hlushchanka (UCLA)

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

]]>Speaker(s): Eamon Quinlan (University of Michigan)

]]>Speaker(s): Tarek Elgindi (UC San Diego)

]]>TBA Speaker(s): JÃ¶rn Zimmerling (University of Michigan)

]]>Speaker(s): Brendon Rhoades (UC San Diego)

]]>Speaker(s): Jeffrey Meyer (CSUSB)

]]>Speaker(s): Sara Lapan (UC Riverside)

]]>Speaker(s): Charlotte Chan (Princeton University)

]]>Speaker(s): Alexander Smith (Harvard University)

]]>Speaker(s): Alexander Smith (Harvard)

]]>Speaker(s): Shuoqing Deng (UM)

]]>Speaker(s): Ara Basmajian (CUNY)

]]>TBA

]]>Speaker(s): Christopher Eur (UC Berkeley)

]]>In this talk I will give a brief overview of current academic research on FinTech by using tools from mathematics and statistics. The topics to be discussed include: (1) Designing stable coins: how to design stable cryptocurrency by using option pricing theory. (2) P2P equity financing: how to design contracts suitable for a P2P equity financing platform with information asymmetry. (3) Data privacy preservation: how to do econometrics based on the encrypted data while still preserving privacy. (4) Crowd wisdom and prediction markets: how to use the collective opinion of a group to make predictions. All the above 4 topics are based on my recent papers. Speaker(s): Steve Kou (Boston University)

]]>Speaker(s): Krishnan Shankar (U Oklahoma/NSF)

]]>Speaker(s): Alexander Smith (Harvard University)

]]>Speaker(s): Amir Mohammadi (UCSD)

]]>Speaker(s): Alexander Smith (Harvard University)

]]>Speaker(s): Alexander Smith (Harvard University)

]]> Mathematical Aspects of Arbitrage

We introduce models for financial markets and, in their context, the notions of portfolio rules and of arbitrage. The absence of arbitrage is a central requirement in the modern theories of mathematical economics and finance, as is the even stronger notion of equivalent martingale measure. We relate this to probabilistic concepts such as fair game, martingales, and coherence in the sense of de Finetti.

We also survey a newer, descriptive approach to finance, based on the existence of a growth-optimal portfolio (equivalently, of a portfolio with the so-called â€œnumeraireâ€ property). These equivalent notions proscribe only egregious forms of arbitrage, and lead to an entire theory for the subject which is flexible and simple, allows the outperformance of one portfolio by another, and is able to deal with an arbitrary number of assets. This part of the talk is based on a book in preparation, with Constantinos Kardaras. Speaker(s): Ioannis Karatzas (Columbia University)

Speaker(s): Amir Mohammadi (UCSD)

]]>We provide a detailed probabilistic interpretation, based on stochastic calculus, for the variational characterization of conservative diffusion as entropic gradient flux. Jordan, Kinderlehrer, and Otto showed in 1998 that, for diffusions of Langevin-Smoluchowski type, the Fokker-Planck probability density flow minimizes the rate of relative entropy dissipation, as measured by the distance traveled in terms of the quadratic Wasserstein metric in the ambient space of configurations. Using a very direct perturbation analysis we obtain novel, stochastic-process versions of such features. These are valid along almost every trajectory of the diffusive motion, in both the forward and, most transparently, the backward, directions of time. The original results follow then simply by taking expectations. As a bonus of the approach we obtain the HWI inequality of Otto and Villani relating relative entropy, Fisher information, and Wasserstein distance; and from it the celebrated log-Sobolev, Talagrand and Poincare inequalities of functional analysis. (Joint work with W. Schachermayer and B. Tschiderer.) Speaker(s): Ioannis Karatzas (Columbia University)

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

]]>In a pioneering article from 1981, Harrison and Shepp provided a stochastic integral equation characterizing the skew Brownian motion of Ito & McKean (1963). We provide similar characterizations for skew-reflected scalar semimartingales, and for a class of planar processes with a roundhouse singularity at the origin which we call â€œWalsh semimartingalesâ€ and which include the Walsh Brownian motion as a special case. Armed with this description, and with an associated stochastic calculus that we develop, we formulate and solve problems of optimal control with discretionary stopping for such Walsh semimartingales. (Joint work with Tomoyuki Ichiba, Vilmos Prokaj and Minghan Yan.)

Speaker(s): Ioannis Karatzas (Columbia University)

Speaker(s): Jordan Keller (Harvard, Black Hole Initiative, Cambridge MA)

]]>Granular matter is ubiquitous in nature and exhibits a variety of nontrivial phenomena. In addition, granular medium is intrinsically far from equilibrium, as particles collide inelastically, and a continuous energy input is required to ensure a steady state. Within the same system, different regions of granular media can be at a solid or a gas phase. Here we focus on a granular Leidenfrost effect: a solid-like cluster is levitating above the "hotâ€ granular gas [1]. This state was observed experimentally, when granular matter was vertically vibrated in a two-dimensional container [2]. The solid-gas coexistence can be described by using granular hydrodynamics with the properly measured transport coefficients [3]. We performed extensive molecular dynamics simulations of a simple model of inelastic hard spheres driven by a â€œthermalâ€ bottom wall. Simulations showed that for low wall temperatures, the levitating cluster is stable, while for high wall temperatures, it breaks down, and the hot gas bursts out resembling a volcanic explosion [4]. We found a hysteresis: for a wide range of bottom wall temperatures, both the clustering state and the broken state are stable. However, even if the system is at the (stable) clustering state, a "volcanic explosion" is possible: it is a rare event driven by large fluctuations. We used techniques from the theory of rare events to compute the mean time for cluster breaking to occur; this required the introduction of a two-component reaction coordinate [4].

[1] B. Meerson, T. PÃ¶schel, and Y. Bromberg, Phys. Rev. Lett. 91, 024301 (2003).

[2] P. Eshuis, K. van der Weele, D. van der Meer, and D. Lohse, Phys. Rev. Lett. 95, 258001 (2005); N. Rivas, A.R. Thornton, S. Luding, and D. van der Meer, Phys. Rev. E 91, 042202 (2015).

[3] E. Khain, Phys. Rev. E 98, 012903 (2018).

[4] E. Khain and L. M. Sander, Phys. Rev. E 94, 032905 (2016).

Speaker(s): Evgeniy Khain (Oakland University)

Quasiregular mappings are only differentiable almost everywhere. There is, however, a satisfactory replacement for the derivative at points of nondiffferentiability. These are generalized derivatives and were introduced by Gutlyanskii et al in 2000. In this talk, we discuss some recent results on generalized derivatives, in particular the question of how many generalized derivatives there can be at a particular point, and explain how versions of the Chain Rule and Inverse Function Formula hold in this setting. We also give some applications to Schroeder functional equations. Speaker(s): Alastair Fletcher (Northern Illinois University)

]]>Speaker(s): Vefa Goksel (UWisconsin)

]]>Speaker(s): CRLT

]]>Speaker(s): Alex Perry (IAS, Princeton)

]]>Deep learning has revolutionized image, text, and speech recognition. Motivated by this success, there is growing interest in developing deep learning methods for financial applications. We will present some of our recent results in this area. In the second part of the seminar, we will study single-layer neural networks with the Xavier initialization in the asymptotic regime of large numbers of hidden units and large numbers of stochastic gradient descent training steps. We prove the neural network converges in distribution to a random ODE with a Gaussian distribution using mean field analysis. Although the pre-limit problem of optimizing a neural network is non-convex (and therefore the neural network may converge to a local minimum), the limit equation minimizes a (quadratic) convex objective function and therefore converges to a global minimum. Furthermore, under reasonable assumptions, the matrix in the limiting quadratic objective function is positive definite and thus the neural network (in the limit) will converge to a global minimum with zero loss on the training set. Speaker(s): Justin Sirignano (UIUC)

]]>Speaker(s): Alex Perry (IAS)

]]>Speaker(s): Giovanni Russo (University of Catania)

]]>Speaker(s): David Galvin (University of Notre Dame)

]]>Speaker(s): Rita Gitik

]]>Speaker(s): Michael Lipnowski (McGill University)

]]>Speaker(s): Dave Goldberg (Cornell)

]]>Speaker(s): David Nordsletten (University of Michigan, Biomedical Engineering and Cardiac Surgery)

]]>Speaker(s): Emily Barnard (De Paul University)

]]>

With the application of machine learning techniques growing in popularity, we will discuss challenges that arise when using these techniques in the financial industry. Some of these challenges, like choosing a good objective function and the avoidance of overfitting, are encountered in most applications of machine learning. Other challenges are unique to finance, namely high frequency trading. These include accounting for correlated risk and deploying models in an environment where latency and throughput affect model performance. In this talk, we will explore both types of challenges and illustrate concepts using simple toy models.

Speaker(s): Chris Hammond (Susquehanna International Group)

Speaker(s): Fall Break

]]>Speaker(s): Margaret Bilu (New York University)

]]>TBA

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

]]>Speaker(s): Jeffrey Diller (University of Notre Dame)

]]>Speaker(s): Sam Payne (University of Texas at Austin)

]]>Speaker(s): Yunqing Tang (IAS)

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

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

]]>Speaker(s): Jinchao Xu (Penn State University)

]]>Speaker(s): Chelsea Walton (University of Illinois)

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

]]>Speaker(s): Bernhardt Thomas (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 information on the U-M Department of Physics website:https://lsa.umich.edu/physics/news-events/special-lectures/ta-you-wu-lecture.html

Speaker(s): Jun Zhang (University of Michigan)

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

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

]]>Speaker(s): Richard Rimanyi (University of North Carolina)

]]>Speaker(s): Richard Rimanyi (University of North Carolina)

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

]]>Speaker(s): Shigeyuki Kondo (Nagoya University)

]]>Speaker(s): Robert McCann (University of Toronto)

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

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

]]>TBA

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

]]>Speaker(s): Vladimir Sverak (University of Minnesota)

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

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

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

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

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

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

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

]]>Speaker(s): CRLT

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

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

]]>Speaker(s): Winter Break

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

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

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

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

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

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