Abstract:

Quantum devices could perform some informational tasks with much better performances than classical systems, with profound implications for cryptography, chemistry, material science, and many areas of physics. However, to reach this goal we need to control large quantum systems, where the many-body dynamics might scramble the quantum information, heating up the system to its thermal state.

There are then two key questions:

- How does a closed quantum system thermalize (thus losing its “quantum power”)?

- How can we preserve quantum information in the presence of strong interactions, disorder, and noise?

Using spins as an exemplary experimental system, I will show how to choreograph their dynamics in order to prevent the system from heating up, even in the presence of strong interactions among spins. I will further show how we can turn disorder from a source of noise to a tool that enables probing the system at the angstrom level. An exemplary application is the creation and characterization of a robust time crystal.

Bio:

Paola Cappellaro is Professor of Nuclear Science and Engineering at the Massachusetts Institute of Technology and a member of the Research Lab for Electronics, where she leads the Quantum Engineering Group. She received her Ph.D in 2006 from MIT and she then joined Harvard University as a postdoctoral associate in the Institute for Theoretical Atomic, Molecular and Optical Physics (ITAMP), before going back to MIT as a faculty in 2009.

Prof. Cappellaro is an expert in NMR, ESR, coherent control and quantum information science. She is a specialist in spin-based quantum information processing and precision measurements in the solid state. With collaborators, she developed the concept and first demonstrations of NV-diamond magnetometers. Cappellaro's major contributions have been in developing control techniques for nuclear and electronic spin qubits, including NV-diamond, inspired by NMR techniques and quantum information ideas. The goal is the realization of practical quantum nano-devices, such as sensors and simulators, more powerful than their classical counterparts, as well as the acquisition of a deeper knowledge of quantum systems and their environment. Her work has been recently recognized by the Young Investigator Award from the Air Force Office of Scientific Research and a Merkator Fellowship.

The smooth fine curve graph of a surface is an analogue of the fine curve graph that only contains smooth curves. It is natural to guess that the automorphism group of the smooth fine curve graph is isomorphic to the diffeomorphism group of the surface. But it has recently been shown that this is not the case. In this talk, I will give several more examples with increasingly wild behavior and give a characterization of this automorphism group for the particular case of continuously differentiable curves.

]]>Topological insulators are striking quantum materials which block electricity in their interior but support robust currents along their boundary. The bulk-edge correspondence is a physical principle that expresses the conductance of the boundary in terms of a bulk topological invariant. We will give a state-of-the-art review of the subject, including recent results in collaboration with Xiaowen Zhu.

This talk will be on Zoom.

Join Zoom Meeting

https://umich.zoom.us/j/92322777234

Meeting ID: 923 2277 7234

Passcode: 878188

October 10:

Speaker: Nathan Li

Title: Characteristic Classes

Abstract: Characteristic classes are cohomological invariants of vector bundles. In this talk, I will give an overview of the Stiefel-Whitney classes and their applications, including showing the tangent bundle of an orientable 3-manifold is trivial.

On behalf of the organizers, please join MCAIM, DCMB and ASC in celebrating Dan Burns, Professor of Mathematics, at a conference in his honor on Friday, October 11, 2024, at the Michigan Union.

Burnsfest: Fostering Mathematical Connections with Africa and Medicine will include a morning session on mathematical partnerships with Africa and an afternoon session on mathematical medicine and biology.

Please register on the conference web site: https://sites.lsa.umich.edu/burnsfest/

Abstract: Generative modeling represents one of the most striking examples of the successes of modern machine learning. In generative modeling, one seeks to artificially generate new data that belongs to given input class. For instance, generating new faces from a database of celebrity faces. Mathematically, this can be posed as finding a map that pushes a simple concrete probability distribution, such as a standard Gaussian, to a complicated abstract distribution that is only known through examples.

Currently, one of the most popular paradigms in generative modeling is diffusion modeling, where the map is constructed by reversing the flow of a diffusion equation applied to the example set. The standard approach in the literature focuses on flowing along a Fokker-Planck equation (i.e. a heat equation with a drift term) and requires stochasticity in the backwards flow to prove convergence rates. In this talk, I will discuss some advantages of flowing along a more general class of diffusion equations and prove convergence rates when the backwards flow is deterministic.

Contact: Selim Esedoglu.

Motivated by our search for a representation-theoretic avatar of double Grothendieck polynomials G_w(x;y), we give a new formula for G_w(x;y) based on Magyar's orthodontia algorithm for diagrams. We obtain a similar formula for double Schubert polynomials S_w(x;y), and a curious positivity result: For vexillary permutations w, the polynomial x_1^n \dots x_n^n S_w(x_n^{-1}, \dots, x_1^{-1}; 1, \dots, 1) is a graded nonnegative sum of Lascoux polynomials. This is joint work with Avery St. Dizier.

]]>The generic vanishing theorem says that the cohomology of a generic topologically trivial line bundle vanishes in all degrees less than the Albanese dimension of the variety. It is a very useful tool in the study of irregular varieties and abelian varieties. In this talk, we will introduce this theorem and its applications.

]]>In this talk, I will discuss my joint work with Michael Bersudsky and Hao Xing extending Ratner’s theorem on equidistribution of individual orbits of unipotent flows on finite volume homogeneous spaces of Lie groups to trajectories of non-contracting curves definable in a polynomially bounded o-minimal structure.

To be precise, let φ : [0, ∞) → SL(n, R) be a continuous map whose coordinate functions are definable in a polynomially bounded o-minimal structure; for example, rational functions. Suppose that φ is non-contracting:

∀ linearly independent v1,...,vk ∈ R^n, φ(t) (v1∧···∧vk)̸→0 as t→∞.

Then, there exists a unique smallest subgroup H_φ of SL(n, R) generated by unipotent one-parameter subgroups such that

φ(t) H_φ → g_0 H_φ in SL(n, R)/H_φ as t→∞ for some g_0 ∈SL(n,R).

For any Lie subgroup G of SL(n,R) such that φ([0,∞)) ⊂ G, we have H_φ ⊂G. For any lattice Γ in G and x∈G/Γ, the trajectory { φ(t)x:t≥0} gets equidistributed with respect to the measure g_0.μ_F_x, where H_φ x = Fx for a closed connected subgroup F of G and μ_F_x is the unique F-invariant probability measure on Fx.

Ample line bundles on schemes have many equivalent characterizations, but one key feature is that they can be used to embed the base scheme into a projective space. I will present two natural definitions of an ample vector bundle on a stack, not clearly equivalent, one generalizing a cohomological property and the other generalizing the embedding property of ample line bundles. Using the latter, and extending work of Kresch, I will explain how an ample vector bundle on a tame stack induces an embedding into [V^s/GL_r] where V^s is the twisted affine GIT stable locus in some polynomial representation V of GL_r. An application is the construction of moduli of stacks with ample vector bundle and in particular a very general stack of tame stacky curves. This is joint with Daniel Bragg and Martin Olsson.

]]>In this talk, we discuss about the smooth random dynamical systems on surfaces. Based on the measure rigidity work by Aaron Brown and Federico Rodriguez Hertz, we know that a stationary measure has SRB property unless there is a certain obstruction. Here, SRB property implies that, morally, the measure is 'absolutely continuous' along 1 dimensional piece.

In this talk, we consider about a different mechanism to get ‘measure rigidity’ which promote SRB to absolute continuity using ‘transversality' motivated by Tsujii’s works on partially hyperbolic endomorphisms and Bernoulli convolution.

The talk is based on a joint work in progress with Aaron Brown, Davi Obata, and Yuping Ruan.

Abstract:

Attosecond physics looks into ultrafast light-matter interactions, with high-harmonic generation (HHG) as its hallmark effect. It relies on intense classical (coherent-state) laser light with large photon numbers, while quantum optics usually operates with low photon numbers and non-classical quantum states. In my talk, I will present two works that bridge between attosecond physics and quantum optics. In the first work, we successfully replace the classical (coherent-state) laser pulses by intense non-classical light – bright squeezed vacuum (BSV) – to drive HHG in solids. We show how the BSV’s extremely noisy photon statistics is transferred to its harmonics, leading to a strong enhancement of the harmonic yield and enabling studies of electron-hole dynamics at extreme intensities. In a second work, we measure the Wigner function of a harmonic driven by classical (coherent-state) light in the non-perturbative regime, showing that the quantum state of the harmonic is not trivial. Our work bears the prospect of extending the frontier of quantum optics and non-classical light into the extreme-ultraviolet spectral regime.

Bio:

Dr. Michael Krueger joined the Technion as an assistant professor of Physics in 2019. He received his Ph.D. from the Ludwig Maximilian University in Munich, Germany, in 2013. From 2014 to 2019, he performed postdoc research at the Weizmann Institute in Rehovot, Israel. In his research, Michael studies ultrafast quantum phenomena on the nanoscale. His main scientific achievements resulting from his Ph.D. have laid the foundation for the integration of attosecond science and nanoscience. This advancement could lead to novel microscopy approaches with extreme time resolution. For his Ph.D. work, Michael received the Otto Hahn Medal of the Max Planck Society in 2015. For his research at Technion, he has been awarded with a Starting Grant of the European Research Council.

The homotopy fixed points of Lubin-Tate theories are central objects in chromatic homotopy theory, as they are building blocks of K(n)-local spheres. This talk will describe the use of equivariant structure and vanishing line result to compute the RO(Q_8)-graded homotopy fixed points spectral sequence at height 2 and prime 2. This is joint work with Zhipeng Duan, Hana Jia Kong, Guchuan Li, and Guozhen Wang.

]]>October 10:

Speaker: Nathan Li

Title: Characteristic Classes

Abstract: Characteristic classes are cohomological invariants of vector bundles. In this talk, I will give an overview of the Stiefel-Whitney classes and their applications, including showing the tangent bundle of an orientable 3-manifold is trivial.

This talk concerns the Benjamin-Ono (BO) equation of internal wave theory, and properties of the solution of the Cauchy initial-value problem in the situation that the initial data is fixed but the coefficient of the nonlocal dispersive term in the equation is allowed to tend to zero (i.e., the zero-dispersion limit). It is well-known that existence of a limit requires the weak topology because high-frequency oscillations appear even though they are not present in the initial data. Physically, this phenomenon corresponds to the generation of a dispersive shock wave. In the setting of the Korteweg-de Vries (KdV) equation, it has been shown that dispersive shock waves exhibit a universal form independent of initial data near the two edges of the dispersive shock wave, and also near the gradient catastrophe point for the inviscid Burgers equation from which the shock wave forms. In this talk, we will present corresponding universality results for the BO equation. These have quite a different character than in the KdV case; while for KdV one has universal wave profiles expressed in terms of solutions of Painlevé-type equations, for BO one instead has expressions in terms of classical Airy functions and Pearcey integrals. These results are proved for general rational initial data using a new approach based on an explicit formula for the solution of the Cauchy problem for BO. This is joint work with Elliot Blackstone, Louise Gassot, Patrick Gérard, and Matthew Mitchell.

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]]>Higher rank lattices, for instance, SLnZ with n greater than 2, are expected to be rigid in many cases. In this talk, we will discuss about actions on manifolds by higher rank lattices under the dynamical assumption (existence of positive (topological) entropy element). We will focus on, how, under certain assumptions, one can obtain information about the action group. We will also see that how one can obtain ‘’homogeneous'' structure of the manifold from the dynamics.

The talk is based on a joint work with Aaron Brown.

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]]>Quantum optics is the quantum theory of the interaction of light and matter. This talk will present a survey of recent results on related many-body problems involving the transport of entangled photons in a system of two-level atoms. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.

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]]>Scalable Rydberg atom arrays are a fast evolving platform for programmable quantum computation and simulation. We present a new system for the control of 2D Rydberg atom arrays embedded in a cryogenic environment. Our high optical access system is compatible with long vacuum lifetime, high-fidelity atomic manipulation, and reduction of blackbody-driven Rydberg decay. I present measurements of ground-state and initial Rydberg manipulation in our cold box, as well as long-lived atoms in a cryopumped vacuum with which we study single-atom imaging of rubidium with high survival, an important component of high-fidelity atom rearrangement. I discuss plans to harness similar long-lived vacuum conditions for addressing one source of loss and heating in Fermi gases. I also outline our ongoing efforts in controlling external degrees of freedom in an optical tweezer traps in the context of cooling, light-assisted collisions, and non-classical motional states.

]]>October 10:

Speaker: Nathan Li

Title: Characteristic Classes

Abstract: Characteristic classes are cohomological invariants of vector bundles. In this talk, I will give an overview of the Stiefel-Whitney classes and their applications, including showing the tangent bundle of an orientable 3-manifold is trivial.

Abstract: Swarmalators are active particles that have internal phases and also swarm through space. Phase synchronization is affected by spatial arrangement, and spatial motion is affected by phase synchronization. Swarmalators have recently been realized in robotics labs, and may also play a role in describing collective behavior of biological organisms. In this work I will describe the effects of time delay in interactions on collective dynamics of a population of swarmalators. Delay resulted in the appearance of new collective states. One such state is a pseudo-crystaline structure - in which swarmalators form a quasi-static cluster, and another is a boiling state in which swarmalators near the boundary of the cluster perform convective motions. In both cases, the route to these states takes place through an oscillatory transient in which the whole cluster “breathes”. Remarkably, just a pair of nonlinear equations (in a system of N swarmalators) describes the behavior of the cluster during this transient. This system also exhibits an intriguing aging phenomenon. I will describe the specific mechanism by which the system ages - which involves gradual increase in the hexatic order parameter, accompanied by a series of annihilations of coordination number defect pairs.

Contact: Evgeniy Khain (Oakland University)

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]]>In the Math LCIT, individuals interested in inclusive teaching in mathematics meet to discuss topics related to this subject. Details of each meeting are found on the U(M) Math Learning Community on Inclusive Teaching page, which is included in the links for this event.

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Speaker: Nathan Li

Title: Characteristic Classes

Abstract: Characteristic classes are cohomological invariants of vector bundles. In this talk, I will give an overview of the Stiefel-Whitney classes and their applications, including showing the tangent bundle of an orientable 3-manifold is trivial.

The US political arena is generally a bleak mix of distressing and aggravating, particularly in the current highly polarized climate, but that distress only increases the need to honestly and scientifically understand the forces at play in ideological space, and the polarization offers emergent simplicity and thus a unique opportunity for mathematical modeling. This talk will share some recent and ongoing attempts to visualize and understand the current political landscape, as well as some quantitative patterns in political psychology and the modern information ecosystem. These recently-gathered data inform a mechanistic dynamical model of ideological drift, allowing theory to extrapolate the complex implications of micro-scale data to macro-scale outcomes---while iteratively improving and suggesting further data-gathering efforts to corner remaining uncertainty. The first waves of results from this perspective provide some remarkable insights, providing some hope of understanding and productively informing political messaging and algorithmic design for a more reasonable political future.

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Speaker: Nathan Li

Title: Characteristic Classes

Abstract: Characteristic classes are cohomological invariants of vector bundles. In this talk, I will give an overview of the Stiefel-Whitney classes and their applications, including showing the tangent bundle of an orientable 3-manifold is trivial.

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]]>This is a one day conference that travels around the Midwest; this Fall, we are hosting it in Ann Arbor.

The speakers will be

Chris Eur (Carnegie Mellon University)

Patricia Klein (Texas A&M University)

Matt Larson (Princeton / Institute for Advanced Study)

Jianping Pan (North Carolina State University)

There will also be a poster fair; you can sign up to present a poster!

To register for ALGECOM, please fill out the google poll at

https://forms.gle/BVe3MHfckc8kXTkn9

If you are applying for financial support, please fill out the form before October 1 in order to be considered. However, please do fill out the form if you think you will come, even if you are local and don't need support; it is helpful to us to know who will be coming.

The ALGECOM organizers are

David Speyer (U Michigan)

Peter Tingley (Loyola)

Alex Yong (UIUC)

Abstract:

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]]>Mean field games model the strategic interaction among a large number of players by reducing the problem to two entities: the statistical distribution of all players on the one hand and a representative player on the other. The master equation, introduce by Lions, models this interaction in a single equation, whose independent variables are time, state, and distribution. It can be viewed as a nonlinear transport equation on an infinite dimensional space. Solving this transport equation by the method of characteristics is essentially equivalent to finding the unique Nash equilibrium. When the equilibrium is not unique, we seek selection principles, i.e. how to determine which equilibrium players should follow in practice. A natural question, from the mathematical point of view, is whether entropy solutions can be used as a selection principle. We will examine certain classes of mean field games to show that the question is rather subtle and yields both positive and negative results.

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]]>In the Math LCIT, individuals interested in inclusive teaching in mathematics meet to discuss topics related to this subject. Details of each meeting are found on the U(M) Math Learning Community on Inclusive Teaching page, which is included in the links for this event.

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Speaker: Nathan Li

Title: Characteristic Classes

Abstract: Characteristic classes are cohomological invariants of vector bundles. In this talk, I will give an overview of the Stiefel-Whitney classes and their applications, including showing the tangent bundle of an orientable 3-manifold is trivial.

Abstract TBA.

Contact: Robert Krasny.

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]]>It will initially be considered the asymptotic behavior of the solution of a mean-field system of Backward Stochastic Differential Equations with Jumps (BSDEs), as the multitude of the system equations grows to infinity, to independent and identically distributed (IID) solutions of McKean–Vlasov BSDEs. This property is known in the literature as backward propagation of chaos. Afterwards, it will be provided the suitable framework for the stability of the aforementioned property to hold. In other words, assuming a sequence of mean-field systems of BSDEs which propagate chaos, then their solutions, as the multitude of the system equations grows to infinity, approximates an IID sequence of solutions of the limiting McKean–Vlasov BSDE. The generality of the framework allows to incorporate either discrete-time or continuous-time approximating mean-field BSDE systems.

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This talk will take place on Zoom and will be broadcast in EH 3866.

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Speaker: Nathan Li

Title: Characteristic Classes

Abstract: Characteristic classes are cohomological invariants of vector bundles. In this talk, I will give an overview of the Stiefel-Whitney classes and their applications, including showing the tangent bundle of an orientable 3-manifold is trivial.

Abstract TBA.

Contact: Selim Esedoglu

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Speaker: Nathan Li

Title: Characteristic Classes

Abstract: Characteristic classes are cohomological invariants of vector bundles. In this talk, I will give an overview of the Stiefel-Whitney classes and their applications, including showing the tangent bundle of an orientable 3-manifold is trivial.

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]]>In this talk I will present a principal-agent problem in continuous time with multiple lump-sum payments (contracts) paid at different deterministic times. Based on the approach introduced in Cvitanić-Possamai-Touzi, we reduce the non-zero sum Stackelberg game between the principal and agent to a standard stochastic optimal control problem. We apply our result to a benchmark model for which we investigate how different inputs (payment frequencies, payment distribution, discount factors, agent's reservation utility, renegotiation) affect the principal's value. This is a joint work with Erhan Bayraktar, Ibrahim Ekren, and Liwei Huang.

]]>In the Math LCIT, individuals interested in inclusive teaching in mathematics meet to discuss topics related to this subject. Details of each meeting are found on the U(M) Math Learning Community on Inclusive Teaching page, which is included in the links for this event.

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