Female vampire bats regurgitate portions of their blood meals to help unfed bats in need. These food donations occur reciprocally among both kin and nonkin. This observation was a classic textbook example of "reciprocal altruism" (or reciprocity)-- the idea that cooperation is stable because cooperative investments are conditional on cooperative returns. However, this explanation for nonkin sharing has become increasingly controversial over time as various authors have proposed alternative explanations. I will review what is known about how vampire bats make helping decisions and show evidence that food sharing in vampire bats has origins in maternal care and kin selection, but is now stabilized by multiple (possibly interacting) forces of enforcement and assortment. I will highlight the underappreciated factor that the degree of fitness interdependence in social relationships can change continuously over time and that studying how cooperative relationships form provides key insights into their functions.

]]>This talk is an overview of the topic of this semester's learning seminar. It is also a planning meeting as we will also assign speakers to talks.

]]>Title: Tate Classes and Endoscopy for GSp4

Abstract: Weissauer proved using the theory of endoscopy that the Galois representations associated to classical modular forms of weight two appear in the middle cohomology of both a modular curve and a Siegel modular threefold. Correspondingly, there are large families of Tate classes on the product of these two Shimura varieties, and it is natural to ask whether one can construct algebraic cycles giving rise to these Tate classes. It turns out that a natural algebraic cycle generates some, but not all, of the Tate classes: to be precise, it generates exactly the Tate classes which are associated to generic members of the endoscopic L-packets on GSp4. In the non-generic case, one can at least show that all the Tate classes arise from Hodge cycles. I'll explain these results and sketch their proofs, which rely on the theta correspondence.

Talk title and abstract forthcoming

]]>We will schedule talks for the rest of the semester. Suggestions for topics that you would like to hear about and topics you would like to speak about are welcome!

]]>The Pre-Law 101 Info Session is an exploratory program that focuses on developing strategies to explore the legal field and provides an overview of the law school admission process. The session will include a presentation given by AOS Pre-Law Advisors followed by a live Q & A period. The session is open to all interested University of Michigan students and alumni.

Location: EH 1068 in East Hall

A category central to algebraic combinatorics is that of “rings with bases”. We’ll look at a very simple example, the nil Hecke algebra, and its action on polynomials in infinitely many variables. The resulting dual basis is the “Schubert polynomials”. Surprisingly, these have positive coefficients, which we will compute by counting “pipe dreams”.

]]>Everyone who would like to give a talk or would like to suggest a topic for a talk is encouraged to come!

]]>This talk introduces a mean field game for a family of filtering problems related to the classic sequential testing of a Brownian motion’s drift. In our formulation, agents observe a private signal process and want to make a determination about an unknown binary state of nature. The game arises by allowing the drift of the signal process to incorporate information about the other agents’ actions and enforcing that each agent must minimize an associated Bayes risk. In this setting we are able to develop a deep understanding of the solution structure, establish the existence of a mean field equilibrium, and study the equilibria numerically. To the best of our knowledge, this work presents the first treatment in the literature of a tractable mean field game with information filtering, optimal stopping, and a common unobserved noise. This presentation is based on recent joint work with Yuchong Zhang at the University of Toronto.

]]>The Mozes-Shah theorem classifies limits of measures which are invariant under unipotent flows. This is the most common situation that arises in applications of measure classification in Number Theory and Geometry.

I will show some cool examples of this theorem and explain the main steps in the proof of the theorem (relying on the linearization technique of Dani-Margulis).

It will be an RTG talk, mainly focusing on examples.

If time permits I will explain a quantitative version of the theorem due to Einsiedler-Margulis-Venkatesh.

A social stigma emerges from the interaction between specific characteristics deemed different or deviant based on the context specific social norms. This research seeks to understand the experiences of those living with a stigmatized or marginalized identity to improve individual wellbeing, interpersonal relationships, and enhance participation in organizational and academic settings. In this talk, I will discuss how context impacts the experience of stigmatization across two different studies; first by exploring how academic climate at different levels influences career attitudes for marginalized early career scholars. In this study, we suggest that the academic climate within the research group, department, and professional field are important factors for marginalized scholars (e.g., scholars of color, disabled scholars). Second, I will provide an in-depth analysis of stigma identity disclosure through both verbal and nonverbal modalities. Disclosing a concealable stigmatized identity—such as a mental health disorder or sexual assault experience—is a complex process whereby the risk of discrimination is weighed against the burden of concealing. However, little is known how individuals disclose across behavioural modalities, such as language and nonverbal movement dynamics, and situational contexts (e.g., professional settings). Taken together, these studies demonstrate the dynamic nature of stigmatization and propose interventions at multiple levels to improve well-being intra-personally and at the broader systems level.

]]>TBA

]]>We will plan the meetings for the rest of the semester. Please come with a few topics you would be interested in hearing or presenting on.

]]>Putting hyperbolic metrics on a finite-type surface S gives us linear representations of the fundamental group of S into PSL(2,R) with many nice geometric and dynamical properties: for instance they are discrete and faithful, and in fact stably quasi-isometrically embedded.

In this talk, we will introduce (relatively) Anosov representations, which generalise this picture to higher-rank Lie groups such as PSL(d,R) for d>2, giving us a class of (relatively) hyperbolic subgroups there with similarly good geometric and dynamical properties.

This is mostly joint work with Andrew Zimmer.

N/A

]]>Speaker: Steven Kahn

Professor of Mathematics, Wayne State University (WSU)

Co-Founder, WSU Math Corps

Director, WSU Center for Excellence and Equity in Mathematics

Title: Math Corps: Social Justice Through Loving and Believing in Kids--and a few Equations

Abstract: For over 30 years, the Wayne State University Math Corps—through summer camp and Saturday programs—has been working to provide Detroit’s children with the kinds of educational and lifetime opportunities that all children should have. Over the past several years, the Math Corps at U(M) has been doing the same, serving children from Ypsilanti. Rooted in social justice and based on a philosophy of “loving and believing in kids”, the Math Corps has achieved dramatic results and garnered national recognition and widespread acclaim. This talk will examine some of the principles and practices that drive the program, and that have been the most responsible for its success. Specific examples to be highlighted include: the “kids teaching kids” model of teaching and learning, the dedication to building a community that is centered, above all, around kindness, the belief in the importance of humor in all of our daily lives (“Three mathematicians walk into a bar...”), and most importantly, the absolutely unwavering vision that the kids in the Math Corps are all leaders in the fight for a better and more just world.

This event is in-person and online.

Zoom: Meeting ID: 913 4525 9193 Passcode: greatness

Let f be a dominant polynomial transformation of the complex affine plane. The dynamical degree lambda_1 of f is defined as the limit of the n-th root of the degree of the n-th iterate of f. In 2007, Favre and Jonsson showed that the dynamical degree of any polynomial endomorphism of the affine plane is a quadratic integer. For any affine surface S0, there is a definition of the dynamical degree that generalizes the one on the affine plane. We show that the result still holds for any complex affine surface: the dynamical degree of an endomorphism of any complex affine surface is a quadratic integer. The proof uses the space of valuations centered at infinity V. The endomorphism f defines a transformation of V and studying the dynamics of f on V gives information about the dynamics of f on S0. The main result is that under certain hypothesis, f admits an attracting fixed point in V that we call an eigenvaluation. This implies that one can find a good compactification S of S0 such that f admits an attracting fixed point p at infinity and f has a normal form at p; the result on the dynamical degree follows from the normal form.

]]>In a graded ring, a homogeneous ideal is an ideal which is generated by homogeneous elements. This seems straightforward enough, but if your ideal is presented abstractly instead of in terms of generators, it becomes less obvious how to verify homogeneity. In this talk, we will discuss several different techniques for showing an ideal is homogeneous, as well as comparing the strengths and limitations of these techniques. We'll illustrate these via proving useful results on how homogeneity is preserved, such as showing that associated primes of homogeneous ideals are homogeneous ideals, and showing the integral closure of a homogeneous ideal is homogeneous.

]]>Please join us for our planning meeting! We will discuss what topics we want to present/hear this semester. There will be a snack.

Note the unusual time/place.

We start with the Bruhat decomposition of the full flag variety and the Borel presentation of its cohomology ring to introduce the Schubert polynomials, the main objects of interest for this seminar. We will then briefly discuss several topics that can be covered throughout the semester, including various monomial expansions of the Schubert polynomials, combinatorial algebraic geometry of the Schubert varieties, Gröbner geometry of matrix Schubert varieties and more.

]]>The Mordell--Weil Theorem states that the rational points of an abelian variety are finitely generated. The proof is in two steps: first, we will reduce the problem to the weak Mordell--Weil Theorem using the theory of heights. Then we will prove the weak Mordell--Weil Theorem from the finiteness of the Selmer group. The talk will be accessible to anyone who has seen some algebraic number theory.

]]>A metric structure is a metric space equipped with various

functions, relations, and constants. We will introduce metric

structures and signatures, as well as some of the examples to which

continuous logic can be applied.

Sexual satisfaction is a multifaceted construct that consists of physiological responses, interpersonal dynamics, positive affect, and gender-specific socialization. Yet, what sexual satisfaction means to individuals is unclear. Quantification of sex has been an important method for measuring sexual satisfaction in research due to its assumed objectivity. However, it has been argued that an “objective” measure of sexual satisfaction via quantification takes away the ability to critically reflect on what a personal definition of sexual satisfaction is through this reliance on quantification as a default. Importantly, sex and sexual socialization are racialized experiences. Researchers often place white women as the prototype for women’s sexuality while emphasizing the risk paradigm for Black and Brown bodies. Similarly, societal messaging surrounding racial sexual stereotypes hypersexualizes and vilifies some bodies while idolizing others. In this talk, I will discuss how Black, Latina, Afro-Latina and white women described the factors that are important to their sexual satisfaction. My analysis looked at whether there were differences by race-ethnicity group in how women described these factors, and how women relied on quantification (of sex and/or orgasm) when defining sexual satisfaction. Utilizing the framework of intimate justice, I argue that the orgasm imperative and the legitimization of sexuality through quantification impacts women of all racial-ethnic groups, however white women have a buffer of whiteness.

]]>A real form of a complex algebraic variety X is a real algebraic variety whose complexification is isomorphic to X. Many families of complex varieties have a finite number of nonisomorphic real forms, but up until recently no example with infinitely many had been found. In 2018, Lesieutre constructed a projective variety of dimension six with infinitely many nonisomorphic real forms, and this year, Dinh, Oguiso and Yu described projective rational surfaces with infinitely many as well. In this talk, I’ll present the first example of a rational affine surface having uncountably many nonisomorphic real forms.

]]>Introduction and organizational meeting

]]>Unitary Shimura varieties are moduli spaces of abelian varieties with certain extra structures. A fruitful way to study their geometry is by considering stratifications of the space. One such stratification is the Ekedahl-Oort (E-O) stratification defined with respect to the structure of the p-torsion group scheme. We follow the work of Moonen and Wooding to investigate the interaction of the E-O strata with other aspects of the geometry of the Shimura variety. We present a few novel results and observations in some specific cases, as well as some future directions. Time permitting, we'll also talk about the Newton stratification.

]]>Do you have a combinatorics-related picture that you cannot stop thinking about? Bring it next week and share its marvelousness and what it means (or why you want to know what it means) and why you think it's cool -- lightning-talk style!

]]>We may think of degeneration as a way to approximate a given ideal or ring by a possibly simpler ideal or ring. We will begin by understanding degenerations of an ideal in a polynomial ring to a monomial ideal (called Grobner degeneration). Analogously, we will also consider toric degenerations of rings. Finally, we will see some concrete applications of these techniques. Time permitting, we will also discuss different techniques for producing such degenerations.

]]>Tame geometry was suggested by Grothendieck as a possible paradise where the geometer would not have to worry about the existence of pathologies of real analysis. Developed by model theorists as o-minimal geometry, tame geometry has had spectacular applications to algebraic geometry in the last 15 years. This talk will review the key concepts and present some of these applications.

]]>We will be talking about the main ways to compute the Schubert polynomials from permutations, relationships between Schubert polynomials and RC-graphs, chute moves on RC-graphs, and the Monk's rule.

]]>We will introduce the syntax and semantics for continuous

logic, defining the formulas of continuous logic and what it means for

a formula to be true in a metric structure.

We show that given a class of comonotonic claims there is a probability measure Q such that the dynamic spectral risk measure of each such claim is a martingale under Q. The applications explored of this result are: (1) the use of statistical and calibration techniques that are typically employed under the law of one price, such as digital moment estimation and fast Fourier transform; (2) a simplified numerical scheme for the nonlinear valuation of financial claims and of portfolio selection that minimizes the worst case scenario value; (3) the definition of a dynamic, time-consistent, convex, but not coherent spectral risk measure, which allows the introduction of diminishing marginal returns without the theoretical limitations of expected utility theory

]]>Hodge theory, as developed by Deligne and Griffiths, is one of the main tools for analysing the geometry and arithmetic of complex algebraic varieties, that is, solution sets of algebraic equations over the complex numbers. It associates to any complex algebraic variety an apparently simple linear algebra gadget: a finite dimensional vector space over the rationals, whose complexification is naturally endowed with two filtrations. Hodge theory occupies a central position in mathematics through its relations to differential geometry, algebraic geometry, differential equations and number theory.

It is an essential fact that at heart, Hodge theory is not algebraic but rather the transcendental comparison of two algebraic structures. On the other hand, some of the deepest conjectures in mathematics (the Hodge conjecture and the Grothendieck period conjecture) suggest that this transcendence is severely constrained. In these lectures, we survey the recent advances bounding this transcendence, mainly due to the introduction of tame geometry as a natural framework for Hodge theory.

This is the first of a 2-3 part series on elementary Teichmüller theory, and on the SL(2, R) action on related moduli spaces. We will also explore links between the dynamics on Teichmüller space to the dynamics of discrete subgroups of Lie groups on homogeneous spaces.

]]>A lovely feature of algebraic varieties is that they admit compactifications. Even better, it often happens that the geometry of a compactification is influenced, or even determined, by combinatorial data, as occurs in the correspondence between toric varieties (certain compactifications of tori) and fans (combinatorial data). Log geometry is a powerful formalism for keeping track of combinatorial data at the boundary of a compactification, and since its introduction in the 1980's, it has played an important role in a wide range of topics from p-adic Hodge theory to the birational geometry of moduli spaces. The goal of the talk is to give a brief introduction to the basic language of log geometry, with no previous exposure to toric geometry assumed.

]]>The surface group representations of Euler class zero into PSL(2,R) are those which are deformations of diagonal (reducible) representation. Marche'-Wolff showed that the mapping class group acts ergodically on these representations with the strange exception of genus 2. We explore the infinitesimal data describing a deformation from a diagonal representation to an irreducible representation, and examine how the Torelli group acts on these deformations. Joint with James Farre.

]]>Hodge theory, as developed by Deligne and Griffiths, is one of the main tools for analysing the geometry and arithmetic of complex algebraic varieties, that is, solution sets of algebraic equations over the complex numbers. It associates to any complex algebraic variety an apparently simple linear algebra gadget: a finite dimensional vector space over the rationals, whose complexification is naturally endowed with two filtrations. Hodge theory occupies a central position in mathematics through its relations to differential geometry, algebraic geometry, differential equations and number theory.

It is an essential fact that at heart, Hodge theory is not algebraic but rather the transcendental comparison of two algebraic structures. On the other hand, some of the deepest conjectures in mathematics (the Hodge conjecture and the Grothendieck period conjecture) suggest that this transcendence is severely constrained. In these lectures, we survey the recent advances bounding this transcendence, mainly due to the introduction of tame geometry as a natural framework for Hodge theory.

Are you considering applying for an internship? Hear from your peers regarding their experiences!

This is an informal discussion session with a student panel, consisting of AIM PhD students with prior internship experiences. The panel will provide a overview of their respective journeys, and attendees will have nearly the full duration of the seminar to ask questions.

The RSK algorithm gives a beautiful bijection between the symmetric group S_n and pairs of young tableaux with the same shape. In this interactive talk we will see several ways to implement the algorithm, from patience sorting to growth diagrams to geometric constructions. There will be lots of examples (and maybe a little representation theory).

]]>Title: Global Shimura varieties

]]>Roughly 15 years ago, Alexander Katsevich, motivated by tomography, began to study the singular values of the finite Hilbert transform (FHT) acting on interval subsets of the real line. This was the beginning of a (ongoing) program that has produced 10+ papers by 5 authors dedicated to the spectral theory of the FHT. We mention some of the history, the connection to tomography and conclude by discussing our latest result, which deals with the diagonalization of the FHT acting on many intervals with touching endpoints.

]]>Title: Geometry and arithmetic of bielliptic Picard curves

Abstract: I'll describe the very pretty geometry of the curves y^3 =

x^4 + ax^2 + b, and use it to "see" the quaternionic multiplication on

their Prym varieties, giving a very explicit family of QM abelian

surfaces (sometimes called "false elliptic curves"). I'll then

describe a few recent results on the arithmetic of these surfaces: a)

a full classification of all rational torsion points in this family

and b) a proof that the average rank in the corresponding family of

Pryms is at most 3. This is based on joint work with Laga and

Laga-Schembri-Voight.

Toric ideals are ideals of polynomial rings with interesting algebraic, geometric, and combinatorial properties. In this talk, we'll introduce toric ideals and give several examples. We'll show how to determine Groebner bases for them, as well as discuss their applications to algebraic statistics. If time permits, we'll also give a combinatorial method for calculating their syzygies and multigraded Betti numbers.

]]>Berkovich spaces are analogues of complex manifolds when the complex numbers are replaced by a non-Archimedean field, that is, a field satifying the strong triangle inequality.

I will discuss two instances where Berkovich spaces naturally appear within complex geometry. The first concerns the Yau--Tian--Donaldson conjecture, on the existence of Kähler--Einstein metrics on Fano manifolds. The second situation appears in the context of degenerations of Calabi--Yau manifolds, and features conjectures by Strominger--Yau--Zaslow, and Kontsevich--Soibelman.

This is based on joint work with R. Berman, S. Boucksom, J, Hultgren, E. Mazzon, and N. McCleerey.

We introduce combinatorial formulas of (double) Schubert and Grothendieck polynomials based on bumpless pipe dreams and give a combinatorial proof of Monk’s rule for Schubert and double Schubert polynomials using bumpless pipe dreams that generalizes Schensted’s insertion on semi-standard Young tableaux. We also give a bijection between pipe dreams and bumpless pipe dreams and discuss its canonical nature.

]]>We will continue our study of continuous logic by

introducing model-theoretic notions such as theories and elementary

equivalence and the Tarski-Vaught test for continuous logic.

We discuss quantum ergodicity in the Benjamini-Schramm limit. This concerns equidistribution of eigenfunctions of Laplacian-like operators on sequences of spaces which ``converge'' to their common universal cover. We shall be particularly interested in the case when the universal cover is a symmetric space or an affine building (the non-archimedean analogue of a symmetric space). A result of this kind was first proven by Anantharaman-Le Masson for regular graphs and for which the underlying Laplacian-like operator is the adjacency operator. This result was reproven by Brooks-Le Masson-Lindenstrauss using a new technique which has been subsequently adapted to also work for rank one locally symmetric spaces (Le Masson-Sahlsten, Abert-Bergeron-Le Masson) and for higher rank locally symmetric spaces associated to $SL(d, R)$ (Brumley-Matz). We have obtained analogous results for Bruhat-Tits buildings associated to $SL(3, F)$ where $F$ is a non-archimedean local field. We shall discuss the strategy of proof common to all of these examples as well as discuss some of the new techniques introduced to handle the $SL(3, F)$ case.

]]>Define test configurations; Rees construction; Define the Futaki invariant; Intersection-theoretic formula for the Futaki invariant; Definition of K-stability; Examples.

]]>This is the second of a 2-3 part series on elementary Teichmüller theory, and on the SL(2, R) action on related moduli spaces. We will also explore links between the dynamics on Teichmüller space to the dynamics of discrete subgroups of Lie groups on homogeneous spaces.

]]>Ruled surface is one of the most concrete examples we see when studying algebraic surfaces. These are surfaces that admit a fibration by $\PP^{1}$ over a curve. However, ruled surfaces are very boring since they are too easy in various ways. For instance, they can be easily classified, there are no degenerations, the algebraic structure of the fibre does not change, and the canonical bundle is easy to describe.

On the other hand, fibration by elliptic curves is way more entertaining since there are lots of things happening! We can study how the algebraic structure varies, how the fibre degenerates to a singular one, and can describe the canonical bundle in terms of the singular fibres and the moduli.

It turns out that these phenomena for elliptic surfaces can be generalized to many deep results in algebraic geometry such as variation of Hodge structure, degeneration of Hodge structure, adjunction and subadjunction, canonical bundle formula, semipositivity theorems, volume asymptotics and so on.

Despite the fact that elliptic fibrations are related to these profound theories in algebraic geometry, the example itself is very classical and can be understood explicitly. I will talk about these phenomena for elliptic surfaces in various perspectives.

Title: Cohomology of global Shimura varieties and the global correspondence

]]>Surprisingly, the cohomology ring of a complex grassmannian is isomorphic to a quotient of the ring of symmetric polynomials. While a great result in its own right, understanding this cohomology ring can also help solve problems in enumerative geometry. In this talk I will outline a proof of this result, and time permitting, we will also see an application of this in enumerative geometry.

]]>Title: Orbital integrals for gln and smoothening

Abstract: Orbital integral is a fundamental object in the geometric side of the trace formula. A traditional method to study orbital integrals is through Bruhat-Tits building or affine Springer fiber. In this talk, we will propose another method to study orbital integrals using smoothening.

As an application, we will explain a closed formula of the orbital integral for gln with n=2,3 and a new lower bound for a general n. We also propose a conjecture about the estimation of the orbital integral for any n. Our method works for any local field of characteristic 0 or >n. This is a joint work with Sungmun Cho.

The general subject of the talk is spectral theory of discrete (tight-binding) Schrodinger operators on $d$-dimensional lattices. For operators with periodic potentials, it is known that the spectra of such operators are purely absolutely continuous. For random i.i.d. potentials, such as the Anderson model, it is expected and can be proved in many cases that the spectra are almost surely purely point with exponentially decaying eigenfunctions (Anderson localization). Quasiperiodic operators can be placed somewhere in between: depending on the potential sampling function and the Diophantine properties of the frequency and the phase, one can have a large variety of spectral types. We will consider quasiperiodic operators

$$

(H(x)\psi)_n=\epsilon(\Delta\psi)_n+f(x+n\cdot\omega)\psi_n,\quad n\in \mathbb Z^d,

$$

where $\Delta$ is the discrete Laplacian, $\omega$ is a vector with rationally independent components, and $f$ is a $1$-periodic function on $\mathbb R$, monotone on $(0,1)$ with a positive lower bound on the derivative and some additional regularity properties. We will focus on two methods of proving Anderson localization for such operators: a perturbative method based on direct analysis of cancellations in the Rayleigh—Schr\”odinger perturbation series for arbitrary $d$, and a non—perturbative method based on the analysis of Green’s functions for $d=1$, originally developed by S. Jitomirskaya for the almost Mathieu operator.

The talk is based on joint works with S. Krymskii, L. Parnovski, and R. Shterenberg (perturbative methods) and S. Jitomirskaya (non-perturbative methods).

In this talk we will not prove Fermat's Last Theorem, which states that for $n>2$ there are no positive integer solutions to the equation $a^n + b^n = c^n$. There are many ways to not prove this theorem, and our chosen method will be to explain a theorem of Ribet exhibiting 691-torsion in the class group of the 691st cyclotomic field, and then explain why this ruins an otherwise perfectly nice strategy for proving the titular theorem. In the course of failing to produce a proof, we will encounter class field theory, modular forms, abelian varieties, and Galois representations. I will not presuppose knowledge of these concepts and this talk should be accessible to anyone familiar with number fields.

]]>We will introduce the notion of ultraproducts in our setting of continuous logic, which will soon be used in proving the compactness theorem. This talk will also cover some prerequisites to better understand ultrafilters and ultraproducts.

]]>Abstract: Two salient features of empirical temporal (i.e., time-varying) network data are the time-varying nature of network structure itself and heavy-tailed distributions of inter-contact times. Both of them can strongly impact dynamical processes occurring on networks, such as contagion processes, synchronization dynamics, and random walks. In the first part of the talk, I introduce theoretical explanation of heavy-tailed distributions of inter-contact times by state-dynamics modeling approaches in which each node is assumed to switch among a small number of discrete states in a Markovian manner and the nodes' states determine time-dependent edges. This approach is interpretable, facilitates mathematical analyses, and seeds various related mathematical modeling, algorithms, and data analysis (e.g., theorizing on epidemic thresholds, random walks on metapopulation models, inference of mixtures of exponential distributions, new Gillespie algorithms, embedding of temporal network data), some of which we will also discuss. The second part of the talk is on modeling of temporal networks by static networks that switch from one to another at regular time intervals. This approach facilitates analytical understanding of diffusive and epidemic dynamics on temporal networks as well as an efficient algorithm for containing epidemic spreading as convex optimization. Finally, I will touch upon some of my interdisciplinary collaborations including those on static networks.

Event will take place in-person in 4448 East Hall and online via Zoom.

Zoom Webinar Link:

https://umich.zoom.us/j/98734707290

Introduce the space of valuations; Central fiber of test configurations viewed as divisorial valuations.

]]>The Grothendieck ring of varieties over a scheme S is an interesting algebraic construction whose elements are finite type S schemes related by cut-and-paste. We will define this ring, explore some properties, define Motivic invariants with some examples, and explain at the end how these ideas were used in proving a theorem of Kontsevich concerning Hodge numbers of birational Calabi-Yau varieties, using an argument from p-adic integration due to Batyrev.

]]>The active Brownian particle (ABP) model describes a swimmer, synthetic or living, whose direction of swimming is a Brownian motion. The swimming is due to a propulsion force, and the fluctuations are typically thermal in origin. We present a 2D model where the fluctuations arise from nonthermal noise in a propelling force acting at a single point, such as that due to a flagellum. We take the overdamped limit and find several modifications to the traditional ABP model. Since the fluctuating force causes a fluctuating torque, the diffusion tensor describing the process has a coupling between translational and rotational degrees of freedom. An anisotropic particle also exhibits a noise-induced drift. We show that these effects have measurable consequences for the long-time diffusivity of active particles, in particular adding a contribution that is independent of where the force acts. This is joint work with Prof. Jean-Luc Thiffeault.

]]>TBA

]]>Title: TBA

Abstract: TBA

TBA

]]>Title: Adding Vascular Insight to the fMRI Experiment

Abstract: In fMRI data, numerous physiologic sources contribute to the measured signals. We typically aim to model and remove these effects (e.g., heart rate, breathing changes) during data preprocessing, which is itself an active and evolving area of research. However, we can also intentionally amplify physiological processes and characterize their effects in our data. Our lab capitalizes on the strong relationship between respiration and blood flow, using breathing challenges to modulate blood gases and evoke systemic vasodilation that can be characterized throughout the central nervous system using fMRI. With practical adjustments, typical fMRI experiments can simultaneously generate metrics of neural and vascular function, making fMRI a truly multiparametric imaging modality. Vascular insights complement our assessment of neural activity and connectivity in fMRI data, and allow for new exploration into the coupling between neural and vascular physiology. This is extremely valuable information when applying fMRI in a range of neurological pathologies where the vasculature is often implicated in disease and symptom progression. Furthermore, we reveal long-distance coordination of respiratory-driven vasodilation across the brain, which demonstrates network-like organization that mirrors established functional (neural) networks, offering the intriguing potential for "vascular networks" that directly contribute to or interact with brain network function. Finally, we are beginning to adapt these methods to examine neural and vascular function in the cervical spinal cord, with promising results.

*There will be light refreshments.

TBA

]]>We will survey some recent works relating the algebraic degree of optimization problems and the topological Euler characteristics. More specifically, the topological formulas for Maximum Likelihood degree and Euclidean Distance degree will be discussed. We will also explore deeper relations between the algebraic bidegrees in optimization problems and Chern classes. The results are joint works with Laurentiu Maxim, Jose Rodriguez and Lei Wu.

]]>S (volume) and T-invariants of a filtration; Define uniform K-stability.

]]>Motivated by statistical models with varying numbers of parameters, in the past decade there has been an interest in asymptotic phenomena for infinitely many objects such as ideals and algebras related by a group action. We can record detailed quantitative data for infinitely many related objects in a multivariate formal power series, which we call the equivariant Hilbert series. The rational form of these series, if it exists, is of interest as it can provide additional data about the objects in study. In searching for this rational form, we utilize theory of languages and their automata from computer science. For a language and a weight function on it, the sum of weights of words in the language is a multivariate formal power series. This series has a always rational presentation when the language satisfies certain rules determined by a directed graph on a finite number of nodes, commonly known as a regular language. The rational form can be easily computed via the graph. Now, given a family of related algebraic objects, we search for regular languages and weights on them such that their formal power series equals the equivariant Hilbert series for our related objects. The talk will be introductory and is based on is based on https://arxiv.org/abs/2204.07849 and https://arxiv.org/abs/1909.13026. No knowledge on Hilbert series or languages will be assumed.

]]>TBD

]]>N/A

]]>Title: TBA

Abstract: TBA

TBA

]]>TBA

]]>K-stability of canonically polarized and Calabi-Yau varieties; A necessary condition for K-stability.

]]>We develop different models to study the flutter of membranes (of zero bending rigidity) with vortex-sheet wakes in two- and three-dimensional inviscid flows. For 2D flows, we use a nonlinear, time-stepping method to study large-amplitude dynamics in the space of three dimensionless parameters: membrane pretension, mass density, and stretching rigidity. With a linearized version of the membrane-vortex-sheet model we also investigate the instability of a membrane by solving a nonlinear eigenvalue problem iteratively, for three boundary conditions---both ends fixed, one end fixed and one free, and both free. We further consider a simple physical setup: a membrane held by tethers with hinged ends, that interpolates between the fixed--fixed and free--free cases. We additionally study an infinite membrane model mounted on a periodic array of Hookean springs. This model allows us to compute asymptotic scaling laws for how the frequencies, growth rates, and eigenmodes depend on membrane pretension and mass density. Finally, we develop a nonlinear model and computational method to study large-amplitude membrane flutter in 3D inviscid flow for 12 different boundary conditions.

]]>TBD

]]>N/A

]]>Congrats University of Michigan Psychology Grads!

For all graduating Psych and BCN students, come order your cap & gown, graduation announcements, diploma frame, and official class ring at the Grad Fair.

You can also order your regalia online at herff.ly/umpsych.

Dr. John Evans, Certified Mental Performance Consultant, will be discussing the field of sports psychology. He will be exploring options for degrees/certification, his day-to-day experiences working in sport psychology and other tips for students interested in the career.

RSVP: https://myumi.ch/M9qVE

Special test configurations; $\beta$-invariant and Fujita-Li criterion; $\alpha$ and $\delta$-invariants.

]]>Cherry Meyer is an Assistant Professor and holds a joint appointment in the Departments of American Culture (AC) and Linguistics at the University of Michigan Department.

More details to come.

You can also join us on Zoom: https://umich.zoom.us/j/91292768774

N/A

]]>TBA

]]>Title: TBA

Abstract: TBA

TBA

]]>Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences under a discrete-time setting. Motivating examples include nonlinear objectives, state-dependent costs, and regularized optimal transport with general $f$-divergence. Under the bi-causal constraint, we introduce equilibrium transport and characterize it with maximum theorem and extended dynamic programming principle. We apply our framework to study the state dependence of two job markets including top-ranking executives and academia. The empirical analysis shows that a job market with a stronger state dependence is less efficient. The University of California (UC) postdoc job market has the strongest state dependence even than that of top executives, while there is no evidence of state dependence on the UC faculty job market. This is a joint work with Erhan Bayraktar.

]]>Variational approach; Valuations computing $\delta$-invariant; Finite generation.

]]>TBD

]]>N/A

]]>The Thai Student Association at the University of Michigan proudly presents Thai Night 2023!Purchase your tickets now! After a break due to COVID-19, 🇹🇭Thai Night🇹🇭 is back and better than ever! Join us to take a glimpse into Thai culture through exclusive performances and exhibitions, as well as ✨a full-course meal✨ catered by Siam Square!Here's what you should expect:🎤Performances: Thai music (contemporary and traditional), Muay Thai, and MORE!🎨Exhibitions: Thai calligraphy, photo booth, arts and crafts, and MORE!🍲Foods: Pad Thai, green curry, Thai tea, and MORE!⏰When: March 19th, 6:00-8:30pm📌Where: East Hall Psychology Atrium EH 1324Purchase your tickets now!

]]>TBA

]]>Title: TBA

Abstract: TBA

TBD

]]>Learn more about current research and areas of study in the Psych Department, inquire about hands-on research and community opportunities, and connect with faculty and graduate students. This open house event will allow students to personally interact with faculty and grad students to learn more about opportunities within the Psychology Department.

Students interested in finding a position for Winter 2023 should attend the Fall fair (11/15/22). Students interested in finding a position for Sp/Su or Fall 2023 should attend the Winter fair (3/21/23). Everyone is welcome to attend both fairs!

Closer to the event, a list of all participating labs will be sent to everyone who RSVPs here: https://myumi.ch/6NGp8

TBA

]]>Overview; Normalized volume (existence and uniqueness of the minimizer); Boundedness via normalized volume.

]]>TBD

]]>N/A

]]>Title: TBA

Abstract: TBA

TBA

]]>TBA

]]>I will talk about the following question of Gromov: what closed manifolds can be efficiently wrapped with Euclidean wrapping paper? That is, for what M is there a 1-Lipschitz map $\mathbb R^n \to M$ with positive asymptotic degree? Gromov called such manifolds elliptic. We show that, for example, the connected sum of k copies of CP^2 is elliptic if and only if k ≤ 3. I will try to explain the intuition behind this example, how it extends to a more general dichotomy governed by the de Rham cohomology of M, and why ellipticity is central to the program of understanding the relationship between topology and metric properties of maps.

If I have time, I'll also explain why for a non-elliptic M, a maximally efficient map $\mathbb R^n \to M$ must have components at many different frequencies (in a Fourier-analytic sense), and even then it's at best logarithmically far from having positive asymptotic degree. This is joint work with Sasha Berdnikov and Larry Guth.

Openness (via normalized volume); existence of a good moduli; properness and projectivity of K-moduli.

]]>TBD

]]>Note unusual time.

]]>N/A

]]>Title: TBA

Abstract: TBA

Abstract: TBA

]]>Speaker: Marius Beceanu (SUNY, Albany)

]]>TBD

]]>TBD

]]>N/A

]]>Abstract: TBA

]]>TBD

]]>N/A

]]>Title: TBA

Abstract: TBA