Reinterpreting old results, I will show that connective G-spectra for a

finite group G are equivalent to twisted operadic suspensions of E

infinity G-spaces and that connective E infinity ring G-spectra are

equivalent to twisted operadic suspensions of E infinity ring G-spaces. Speaker(s): Peter May (University of Chicago)

We shall be interested in the semiclassical behavior of the scattering

data of a non-self-adjoint Dirac operator with a fairly smooth -but not necessarily

analytic- potential decaying at infinity. In particular, using ideas and methods going

back to Langer and Olver, we provide a rigorous semiclassical analysis of the scattering

coefficients, the Bohr-Sommerfeld condition for the location of the EVs and their

corresponding norming constants. Speaker(s): Nikos Hatzizisis (University of Crete)

I will discuss recent work with Avila and Crovisier (and related work with Eskin, Potrie and Zhang as well) on the following problem and some higher dimensional analogues: Let f be an Anosov diffeomorphism in dimension 3. Assume the unstable bundle is 2 dimensional and admits a dominated splitting into weak and strong unstable bundles. Under what hypotheses is the strong unstable foliation minimal?

Zoom link: https://iu.zoom.us/j/661711533?pwd=RTFVTjMrQ1pYTCtIZzIvVGVvODV2QT09

password is 076877 if needed. Speaker(s): Amie Wilkinson (The University of Chicago)

Zoom link: https://umich.zoom.us/j/99788564257

passcode: -4040 Speaker(s): Bradley Zykoski (University of Michigan)

When I tell people that cubic fourfolds are a hot topic in algebraic geometry, they're often incredulous at what sounds like a random choice of numbers -- why those and not, say, quartic threefolds? But cubic fourfolds are more interesting than hypersurfaces of other degrees and dimensions for two reasons: first, the classical question of which ones are "rational" is unexpectedly hard, lying just out of reach of both old and new techniques; second, they have unexpected connections to K3 surfaces and hyperkähler manifolds, through Hodge theory, derived categories of coherent sheaves, and beautiful geometric constructions. I'll try to give a taste of what has attracted so many people to this topic in the last 15 to 25 years.

The talk will be aimed at a general mathematical audience, including graduate students.

https://msu.zoom.us/j/95343874012

Meeting ID: 953 4387 4012

Passcode: 373396 Speaker(s): Nicolas Addington (University of Oregon)

A classical subject in complex dynamics is the linearization problem, which asks when an analytic function is locally conjugate to its local linearization. This problem has been studied since the 19th century, but it took until the ‘90s to completely resolve the simplest case: quadratic polynomials. In the first part of this talk we will discuss the solution in the quadratic case. In the second part of part of this talk we will examine properties of the Yoccoz function, a remarkable function defined by Yoccoz to study the linearization problem. Speaker(s): Alex Kapiamba (U(M))

]]>Incidence graphs are a tool to keep track of how curves intersect each other in space. Given a collection of curves in projective space, I will explain how to make its incidence graph and discuss some interesting questions that arise. For example, starting with a graph G, can we construct a collection of curves that intersect so that their incidence graph is G? If so, what can we say about the kinds of curves that are needed? No previous experience with graphs, projective space, or algebraic curves needed.

Zoom: https://umich.zoom.us/j/95088797965

Password: cookies Speaker(s): Katie Waddle (University of Michigan)

I will discuss the Hilbert scheme of d points in affine n-space, with some examples. This space has many irreducible components for n at least 3 and has been poorly understood. For n greater than d, we determine the homotopy type of the Hilbert scheme in a range of dimensions. Many questions remain. (Joint with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, Maria Yakerson.) Speaker(s): Burt Totaro (UCLA)

]]>We consider the discretized Bachelier model where hedging is done on an equidistant set of times. Exponential utility indifference prices are studied for path-dependent European options and we compute their non-trivial scaling limit for a large number of trading times $n$ and when risk aversion is scaled like $n\ell$ for some constant $\ell>0$. Our analysis is purely probabilistic. We first use a duality argument to transform the problem into an optimal drift control problem with a penalty term. We further use martingale techniques and strong invariance principles and get that the limiting problem takes the form of a volatility control problem.

(Joint work with Yan Dolinsky)

Speaker(s): Asaf Cohen (UM)

Zoom address: https://umich.zoom.us/j/95135773568

The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. This talk looks at consciousness from the perspective of theoretical computer science. It formalizes the Global Workspace Theory (GWT) originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, and others. Our major contribution lies in the precise formal definition of a Conscious Turing Machine (CTM), also called a Conscious AI. We define the CTM in the spirit of Alan Turing’s simple yet powerful definition of a computer, the Turing Machine (TM). We are not looking for a complex model of the brain nor of cognition but for a simple model of (the admittedly complex concept of) consciousness. After formally defining CTM, we give a formal definition of consciousness in CTM. We then suggest why the CTM has the feeling of consciousness. The reasonableness of the definitions and explanations can be judged by how well they agree with commonly accepted intuitive concepts of

human consciousness, the range of related concepts that the model explains easily and naturally, and the extent of its agreement with scientific evidence.

Hosted by

Department of Computational Medicine & Bioinformatics, Department of Mathematics, University of Michigan

Michigan Institute for Data Science

Smale Institute

BIOS

Lenore has been passionate about mathematics since she was 10. She attributes that to having dropped out of school when she was 9 to wander the world, then hit the ground running when she returned and became fascinated with the Euclidean Algorithm. Her interests turned to non-standard models of mathematics, and of computation. As a graduate student at MIT, she showed how to use saturated model theory to get new results in differential algebra. Later, with Mike Shub and Steve Smale, she developed a foundational theory for computing and complexity over continuous domains such as the real or complex numbers. The theory generalizes the Turing-based theory (for discrete domains) and has been fundamental for computational mathematics. Lenore is internationally known for her work in increasing the participation of girls and women in STEM and is proud that CMU has gender parity in its undergraduate CS program. Lenore Blum lblum@cs.cmu.edu

Manuel has been motivated to understand the mind/body problem since he was in second grade when his teacher told his mom she should not expect him to get past high school. As an undergrad at MIT, he spent a year studying Freud and then apprenticed himself to the great anti-Freud [1] neurophysiologist Warren S. McCulloch, who became his intellectual mentor. When he told Warren (McCulloch) and Walter (Pitts) that he wanted to study consciousness, he was told in no uncertain terms that he was verboten to do so - and why. As a graduate student, he asked and got Marvin (Minsky) to be his thesis advisor. Manuel is one of the founders of complexity theory, a Turing Award winner, and has mentored many in the field who have chartered new directions ranging from computational learning, cryptography, zero knowledge, interactive proofs, proof checkers, and human computation. Manuel Blum mblum@cs.cmu.edu Speaker(s): Lenore Blum & Manuel Blum (Carnegie Mellon)

Speaker(s): Andy Jiang

]]>Speaker(s): Bobby Laudone (UM)

]]>In the talk I will define braid varieties, a class of affine algebraic varieties associated to positive braids, and develop a Soergel-like diagrammatic calculus for correspondences between them.

This is a joint work with Roger Casals, Mikhail Gorsky and Jose Simental Rodriguez. Speaker(s): Eugene Gorsky (UC Davis)

Speaker(s): Andrej Vilfan (Max Planck Institute)

]]>A very important development in the 1960's was the development of étale cohomology by Grothendieck. It allows us to study the algebro-geometric properties of varieties over finite fields, which need not be topologically intuitive. In this talk, we will motivate and build up towards the definition of étale cohomology, followed by an overview of some nice results. Speaker(s): Sandra Nair (UM)

]]>Speaker(s): Mattias Jonsson

]]>In classical differential geometry, a central question has been whether abstract surfaces with given geometric features can be realized as surfaces in Euclidean space. Inspired by the rich theory of embedded triply periodic minimal surfaces, we seek examples of triply periodic polyhedral surfaces that have an identifiable conformal structure. In particular we are interested in explicit cone metrics on compact Riemann surfaces that have a realization as the quotient of a triply periodic polyhedral surface. Results include examples that shed new light on existing minimal or algebraic surfaces, such as the Schwarz minimal P-, D-surfaces, Fermat's quartic, Schoen's minimal I-WP surface, and Bring's curve.

https://umich.zoom.us/j/98191346410?pwd=aDRxRmhUUElTY2c3UUVJZHZwdVhUUT09

Meeting ID: 981 9134 6410

Passcode: 032225 Speaker(s): Dami Lee (University of Washington)

Speaker(s): Malavika Mukundan (U(M))

]]>Speaker(s): Emanuel Reinecke

]]>Speaker(s): Shivaprasad or Wu

]]>Speaker(s): Danny Stoll (U(M))

]]>Speaker(s): Mircea Mustata

]]>Professor Karen Uhlenbeck is a distinguished mathematician of the highest international stature, specializing in differential geometry, nonlinear partial differential equations, and mathematical physics. At the same time, her mentoring of younger mathematicians, especially women, is legendary.

In addition to a plethora of awards and honors, Professor Uhlenbeck won a MacArthur “Genius” Fellowship, the AMS Steele Prize, and the US National Medal of Science. In 1990, she became the second woman (after Emmy Noether in 1932) to present a plenary lecture at an International Congress of Mathematicians. She is a fellow of the American Academy of Arts and Sciences and the US National Academy of Sciences. In 2019, she won the Abel Prize for "her pioneering achievements in geometric partial differential equations, gauge theory, and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” She is the first woman to win the Abel prize.

Professor Uhlenbeck is one of our most famous alumni: she graduated from U(M) with a BA in Mathematics in 1964. Please join us for a conversation with Professor Karen Uhlenbeck! All are welcome!! Speaker(s): Karen Uhlenbeck

Speaker(s): Shivaprasad or Wu

]]>Speaker(s): James Hotchkiss

]]>Speaker(s): Alex Perry

]]>Speaker(s): John Wettlaufer (Yale University)

]]>Title: Tame geometry and Hodge Theory

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): Huyen Pham (Universite Paris Diderot)

]]>Speaker(s): Huang & Reinecke

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