Speaker: John Urschel (MIT)Title: Nodal Statistics for Graphs and MatricesAbstract:The study of nodal statistics provides insight into the spectral properties of graphs and matrices, drawing strong parallels with classical results in analysis. In this talk, we will give an overview of the field, covering key results on nodal domains and nodal counts for graphs and their connection to known results in the continuous setting. In addition, we will discuss some recent progress towards a complete understanding of the extremal properties of the nodal statistics of a matrix.

Speaker: Anlong Chua (MIT)Title: Two applications of the Kazhdan-Lusztig mapAbstract: Let G be a connected reductive group with Lie algebra 𝖌 and Weyl group W. Let P ⊂ G((t)) be a parahoric subgroup with Levi quotient GP.Using the topology of Lie P , Kazhdan and Lusztig define a map from nilpotent orbits in Lie GP to conjugacy classes in W.I will explain some compatibilities between Kazhdan-Lusztig maps associated to different parahoric subgroups, as well as the Kazhdan-Lusztig map for the Langlands dual. Time permitting, I will sketch that these compatibilities come from studying the W-representation on the cohomology of affine Springer fibers. The main tool is Yun’s Global Springer Theory.We will explore two applications of these compatibilities. The first is an affine analog of the classical picture relating singular supports of IC sheaves on the flag variety with special nilpotent orbits. The second is a resolution of Lusztig’s conjecture that strata can be described by fibers of (parahoric) Kazhdan-Lusztig maps.

We are excited to invite you to a landmark event at MIT: “Menstruation Science: Unlocking the Secrets of the Hormone-Immunity Nexus” on April 9, 2025. This event marks the official launch of Menstruation Science—a pioneering new field dedicated to unraveling the biological complexities of menstruation, gynecological health, immune system differences, and the far-reaching effects of sex hormones on human physiology.Join us as we bring together leading experts to ignite new conversations, drive innovation, and shape the future of this often-overlooked yet critical area of research. April 9 Program:4:00 p.m.: Prof Linda Griffith, Director, MIT Center for Gynepathology Research, “Why MIT is launching a Moonshot for Menstruation Science”4:10.: Dr. Lisa Halvorson, MD, first Gynecology Branch Chief for the National Institutes of Health (NIH), “Menstruation Science: How a 2019 NIH conference energized new research in endometrial biology.”4:30: Dr. Hilary Critchley, Professor of Reproductive Medicine, former Director, Centre for Reproductive Health, University of Edinburgh, “Menstruation Science: Teaming Up Around the World.”5:30: Posters, refreshments6:15: Panel: How “Menstruation Science” will stimulate investment in Women’s HealthDr. Pearl Huang, CEO, Dunad Therapeutics Dr. Steve Palmer, CSO, CelMatix Susan Whitehead, Founding Lifetime Trustee, MIT Corporation Dr. Megan Greenfield, Partner, McKinsey & Co. TBA panelist, Third Rock Ventures7:15 – 8:00: More Posters, more refreshmentsWe look forward to celebrating this exciting launch with you!

Speaker: Anlong ChuaTitle: Two Applications of the Kazhdan-Lusztig mapSeminar Webpage: https://math.mit.edu/lg/

Struggling to stay on track with your writing? This four-session workshop series will help you navigate common challenges and develop strategies for a more productive writing process. We will explore how to manage your time and set realistic expectations, harness perfectionism to your advantage, build a strong working relationship with your dissertation advisor or PI, and use constructive procrastination as a tool for maintaining a healthy writing routine. Each session will be interactive and designed to equip you with practical skills to improve your writing habits.Pre-registration is required to participate and light refreshments will be served.

Speaker: Linus Setiabrata (U. Chicago)Title: Double orthodontia formulas and Lascoux positivityAbstract:Motivated by our search for a representation theoretic avatar for double Grothendieck polynomials, we extend Magyar’s orthodontia formula for Schubert polynomials. Our formula gives a curious positivity result: Writing $\mathfrak S_w(\mathbf x, \mathbf y)$ for a vexillary double Schubert polynomial, the polynomial $x_1^n \dots x_n^n \mathfrak S_w(x_n^{-1}, \dots, x_1^{-1}; 1, \dots, 1)$ is a graded nonnegative sum of Lascoux polynomials. Joint work with Avery St. Dizier.