Speaker: Vasudevan Srinivas (Tata and Univ. of Buffalo)Title: Some finiteness results for the etale fundamental group in positive characteristicsAbstract:This talk will discuss some results on etale fundamental groups of varieties over an algebraically closed field of characteristic p > 0, based on joint work with Hélène Esnault and other coauthors. One result, along with Mark Shusterman, is that the tame fundamental group is finitely presented for such a variety which is the complement of an SNC divisor in a smooth projective variety. A second, along with Jakob Stix, is to give an obstruction for a smooth projective variety to admit a lifting to characteristic 0, in terms of the structure of its etale fundamental group as a profinite group. We will finally touch on some open questions.

Speaker: Kevin Ren (Princeton University) - 3 PM until 4 PM in 4-257Speaker: Anshul Adve (Princeton University) - 4:15 PM until 5:15 PM in 2-131➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖Speaker: Kevin Ren (Princeton University)Title: Sharp discretized projection theorem in ℝ3Abstract: For 0 < s < 2, 0 < t < 3, we define f(s, t) to be the largest number such that for every choice of t-dimensional set K in ℝ3 and s-dimensional set E in S2 that does not concentrate in any great circle, there exists a direction 𝓍 ∈ E such that the projection of K onto the plane normal to 𝓍 has dimension at least f(s, t). The multi-linear Kakeya inequality gives f(s, t) ≥2t\3; Weikun He (following Bourgain) proved that f(s, t) ≥2t\3 + ε for some explicit ε (s, t) > 0. We compute the sharp value of f(s, t) for all 0 < s < 2, 0 < t < 3. Joint with Paige Bright and Hong Wang.➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖Speaker: Anshul Adve (Princeton University)Title: Algebraic equations characterizing hyperbolic surface spectraAbstract: Given a compact hyperbolic surface of fixed genus, together with a suitable choice of orthonormal basis of Laplace eigenforms, one can consider two natural spectral invariants: 1) the Laplace spectrum Λ, and 2) the 3-tensor Cijk representing pointwise multiplication (as a densely defined map L2 × L2 → L2) in the given basis. Which pairs (Λ, C) arise this way? Both Λ and C are highly transcendental objects. Nevertheless, we will give a concrete and almost completely algebraic answer to this question, by writing down necessary and sufficient conditions in the form of equations satisfied by the Laplace eigenvalues and the Cijk . This answer was conjectured by physicists Kravchuk, Mazac, and Pal, who introduced these equations (in an equivalent form) as a rigorous model for the crossing equations in conformal field theory.

Aging Brain Seminar with Aaron Gitler, PhD, Stanford UniversityDate: Tuesday, April 15Time: 4:00pmLocation: 46-3310, Picower Seminar Room (In-person only)Defining ALS Mechanisms at Single Cell ResolutionAmyotrophic lateral sclerosis (ALS) is a devastating human neurodegenerative disease caused by a selective loss of motor neurons from the brain and spinal cord. Intriguingly, in ALS, some motor neurons are vulnerable and others are resistant. We used single-cell transcriptomics and epigenomics to explore the heterogeneity of the spinal cord and to discover the changes that occur during ALS. We identified differentially expressed genes associated with degeneration as well as resilience. Our studies have revealed unexpected diversity in the autonomic nervous system, gradients of fast-and slow-firing motor neuron types within motor pools. These findings provide insight into mechanisms of degeneration, molecular underpinnings of selective vulnerability, and may suggest novel therapeutic strategies. We have also been extending studies on the adult human spinal cord, revealing similar logic as in mouse motor neurons.We also use single cell approaches to define the RNA processing changes associated with ALS pathology. A hallmark pathological feature of ALS is the depletion of RNA-binding protein TDP-43 from the nucleus of neurons in the brain and spinal cord. We discovered that TDP-43 represses a cryptic exon splicing event in the ALS risk gene UNC13A. Loss of TDP-43 from the nucleus causes inclusion of a cryptic exon in UNC13A mRNA and reduced UNC13A protein expression. Our data provide a direct functional link between one of the strongest genetic risk factors for ALS UNC13A genetic variant and loss of TDP-43 function. Beyond cryptic splicing, we have also discovered loss of TDP-43 in ALS leads to widespread alternative polyadenylation changes, impacting expression of disease-relevant genes and providing evidence that alternative polyadenylation is a new facet of TDP-43 pathology.Finally, we use simple model systems like yeast to screen for modifiers of ALS disease proteins TDP-43 and FUS and identified the polyglutamine protein ataxin 2 as a potent modifier. We then identified mutations in the ataxin 2 gene as genetic risk factor for ALS and have pursued studies of ataxin 2 as a therapeutic target.Aaron Gitler is the Stanford Medicine Basic Science Professor in the Department of Genetics at Stanford University. He received his B.S. degree from Penn State University and did his PhD studies on cardiovascular development in the laboratory of Dr. Jonathan Epstein at the University of Pennsylvania. Then he performed his postdoctoral training with Dr. Susan Lindquist at the Whitehead Institute for Biomedical Research and MIT. In 2007, he established his laboratory at the University of Pennsylvania and moved to Stanford in 2012. His laboratory has been using a combination of yeast and human genetics approaches to investigate pathogenic mechanisms of ALS. His laboratory has made several fundamental discoveries into neurodegenerative disease mechanisms. These discoveries include discovery of modifiers of aggregation and cytotoxicity of the FTD/ALS disease protein TDP-43, a mechanism to explain how FTD/ALS-linked TDP-43 mutations affect the protein and contribute to disease, and the discovery of novel genetic contributors to human FTD and ALS, including mutations in the ataxin-2 gene as one of the most common genetic risk factors for ALS and a role of cryptic splicing of UNC13A and other synaptic protein encoding genes as a mechanism in ALS and FTD. Gitler’s work has helped to uncover unexpected and novel therapeutic targets for ALS, including preclinical studies of ataxin-2 as a therapeutic target for sporadic ALS, demonstrating that reduction of ataxin-2 levels markedly extends lifespan in TDP-43 transgenic mice.

AI is powerful, but it can make choices that result in objective errors, contextually inappropriate outputs, and disliked options. This is especially critical when AI-powered systems are used for context- and preference-dominated open-ended AI-assisted tasks—like ideating, summarizing, searching, sensemaking, and the reading and writing of text or code. We need AI-resilient interfaces that help users notice and recover from AI choices that are not right, or not right for them given their goals and context. We have derived design implications from key theories of human cognition to help us build more AI-resilient interfaces and reliable tools from unreliable AI.Join us for an important discussion on this topic on Tuesday, April 15th at 4pm. This talk will walk through two new systems that demonstrate this approach: CorpusStudio, an AI-powered writing environment, and MOCHA, a tool for co-adaptive machine teaching.Bio: Elena L. Glassman is an Assistant Professor of Computer Science at the Harvard John A. Paulson School of Engineering & Applied Sciences, specializing in human-computer interaction. Prior to that, she was a postdoctoral scholar at UC Berkeley, and obtained a BS, MEng, and PhD in Electrical Engineering and Computer Science from MIT. She has been named a Stanley A. Marks & William H. Marks Professor at the Radcliffe Institute for Advanced Study and a National Academy of Sciences Kavli Fellow. Her work has been funded by the NSF, private industry, the Berkeley Institute for Data Science, and the Sloan Research Fellowship. This work has received Best Paper and Honorable Mention awards at top-tier human-computer interaction research venues.This event is co-sponsored by the MIT Schwarzman College of Computing and Laboratory for Information and Decision Systems.

Speaker: Kaelyn Sumigray, YaleHost: The Chipperfield CommitteeTitle: "Collective cell dynamics in epithelial morphogenesis"The Biology Colloquium is a weekly seminar held throughout the academic year — featuring distinguished speakers in many areas of the biological sciences from universities and institutions worldwide. More information on speakers, their affiliations, and titles of their talks will be added as available. Unless otherwise stated, the Colloquium will be held live in Stata 32-123 (Kirsch auditorium) Contact Margaret Cabral with questions.

Title: TBD