Claremont Center for the Mathematical Sciences

Building the Fan of a Toric Variety (Professor Reginald Anderson, Claremont McKenna College)
2023-09-27 16:15 - 17:30 (America/Los_Angeles) | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Title: Building the Fan of a Toric Variety
Speaker: Reginald Anderson, Department of Mathematical Sciences, Claremont McKenna College
Abstract: Roughly speaking, algebraic geometry studies the zero sets of polynomials, which lead to objects called varieties. Since the zero sets of polynomials do not always pass the vertical line test, we enlist other methods to study them besides considering the graph of a function. This is analogous to the use of implicit differentiation in calculus. One such method uses line bundles to understand a variety in terms of its algebraic subspaces. Since the zero sets of polynomials can become complicated in multiple variables over the complex numbers, one simplifying assumption we can impose is that the variety contain a dense, open algebraic torus. This leads to the notion of a toric variety. I will describe the fan of a toric variety for the complex projective line, and mention some recent results concerning toric varieties.

Reginald Anderson received his PhD in mathematics from Kansas State University in May and studies derived categories of toric DM stacks. His research areas include algebraic geometry, homological algebra, and category theory.

Applied Math Seminar: Tin Thien Phan (Los Alamos National Laboratory)
2023-10-02 16:15 - 17:15 | Estella 1021 (Emmy Noether Room), Pomona College, Claremont, CA, 91711, United States
Title: Understanding SARS-CoV-2 viral rebounds with and without treatments.
Abstract: In most instances, the characteristics of SARS-CoV-2 mirror the patterns of an acute infection, with viral load rapidly peaking around 5 days post-infection and subsequently clearing within 2 weeks. However, some individuals show signs of viral recrudescence of up to 10000 viral RNA copies/mL shortly following viral remission. These instances of viral resurgence, distinct from long COVID, are generally resolved within four weeks post-infection and have been observed across varying treatment statuses, vaccination statuses, and viral strains. In this presentation, I will review existing evidence of transient viral rebound and demonstrate that a class of dynamic models that incorporates virus-immune interaction accurately describes transient viral rebound dynamics under different treatment scenarios, including those untreated. While these models all share a simple structure with a unique globally-asymptomatic-stable disease-free equilibrium, the most exciting and relevant aspect hides within their transient phase and remains largely unexplored.

Cellular resolutions of the diagonal and exceptional collections for toric D-M stacks (Reginald Anderson, CMC)
2023-10-03 12:15 - 13:10 | Roberts North 102, CMC
Beilinson gave a resolution of the diagonal for complex projective space, which gives a strong, full exceptional collection of line bundles as a generating set for the derived category of coherent sheaves. Bayer-Popescu-Sturmfels generalized Beilinson’s resolution of the diagonal by giving a cellular resolution of the diagonal for a proper subclass of smooth toric varieties which they called “unimodular.” In joint work with Gabe Kerr, we extended this resolution of the diagonal to smooth projective toric varieties by showing that the cokernel of Bayer-Popescu-Sturmfels’ resolution is torsion with respect to the irrelevant ideal. In this talk, we show that Bayer-Popescu-Sturmfels’ resolution yields a strong, full, exceptional collection of line bundles for unimodular projective toric surfaces, and that our extended resolution of the diagonal yields a strong, full exceptional collection of line bundles for a smooth, non-unimodular projective toric surface.

Claremont Topology Seminar: Julian Chaidez (USC)
2023-10-03 15:00 - 16:00 | Fletcher 110, Pitzer College, 1050 N Mills Ave, Claremont, CA, 91711, United States
Title: Quantum 4-Manifold Invariants Via Trisections
Abstract: I will describe a new family of potentially non-semisimple invariants for compact a 4-manifold whose boundary is equipped with an open book. The invariant is computed using a trisection, along with some additional combing data, and a piece of algebraic data called a Hopf triple. The relationship with other recent works on non-semisimple 4-manifold invariants, like the work of Costantino-Geer-Patureau-Mirand-Virelizier, is not yet clear. This talk is based on joint work with Shawn Cui (Purdue) and Jordan Cotler (Harvard).

Thinking Inside the Box: A combinatorial approach to Schubert Calculus (Sami H. Assaf, USC)
2023-10-04 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Title: Thinking Inside the Box: A combinatorial approach to Schubert Calculus
Speaker: Sami H. Assaf, Department of Mathematics, University of Southern California
Abstract: Given 2 lines in the plane, how many points lie on both? If we rule out the case where the two lines are the same, and we work in projective space so that parallel lines share the point at infinity, then the answer is always the same: 1 point of intersection. Suppose instead we’re given 4 lines in space. How many other lines meet all four of those? Schubert asked, and in some cases answered, such problems in enumerative geometry in his celebrated treatise in 1879. He argued that when the answer is finite, it does not depend on the choice of the linear spaces. Attempts to formalize Schubert’s “Principle of Conversation of Number” have led us to modern Schubert calculus and intersection theory, which has ramifications in geometry, topology, combinatorics, and even string theory. I will survey the history of this field from Schubert to now, highlighting a partial solution that involves enumerating ways of putting numbers in boxes.

Sami Assaf is a Professor of Mathematics and a Gabilan Distinguished Professor of Science and Engineering at the University of Southern California. Her fundamental research in combinatorics, geometry and probability is supported by grants from the National Science Foundation and the Simons Foundation. She has delivered plenary addresses for AMS meetings as well as for the annual Formal Power Series and Algebraic Combinatorics conference. Professor Assaf is recipient of a USC Mentoring Award for Faculty Mentoring Undergraduates, directs a local Math Circle for elementary school students, and currently serves as Director of Graduate Studies for the Department of Mathematics where she works to foster a culture of inclusivity, diversity, and excellence for all students.

GEMS October 7th Session
2023-10-07 10:00 - 12:00 | Shanahan 1480, Harvey Mudd College, 301 Platt Blvd., Claremont, CA, 91711, United States

Applied Math Seminar: Dan Pirjol (Stevens Institute of Technology)
2023-10-09 16:15 - 17:15 | Estella 1021 (Emmy Noether Room), Pomona College, Claremont, CA, 91711, United States
Title: The Hartman-Watson distribution: numerical evaluation and applications in mathematical finance
Abstract: The Hartman-Watson distribution appears in several problems of applied probability and financial mathematics. Most notably, it determines the joint distribution of the time-integral of a geometric Brownian motion and its terminal value. A classical result by Yor (1981) expresses it as a one-dimensional integral which is however difficult to evaluate numerically in the region of interest for financial applications. The talk gives an introduction to the HW distribution and presents an asymptotic expansion which can be used for an efficient numerical evaluation. Two applications from mathematical finance are discussed: Asian options pricing in the Black-Scholes model, and option pricing in the log-normal SABR model.

Claremont Topology Seminar: Christopher Perez (Loyola University New Orleans)
2023-10-10 15:00 - 16:00 | Fletcher 110, Pitzer College, 1050 N Mills Ave, Claremont, CA, 91711, United States
Title: Towers and elementary embeddings in total relatively hyperbolic groups
Abstract: In a remarkable series of papers, Zlil Sela classified the first-order theories of free groups and torsion-free hyperbolic groups using geometric structures he called towers. It was later proved by Chloé Perin that if H is an elementarily embedded subgroup (or elementary submodel) of a torsion-free hyperbolic group G, then G is a tower over H. We prove a generalization of Perin’s result to toral relatively hyperbolic groups using JSJ and shortening techniques.

Equality Cases of Geometric Inequalities (Igor Pak, UCLA)
2023-10-11 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Title: Equality Cases of Geometric Inequalities
Speaker: Igor Pak, Department of Mathematics, University of California, Los Angeles
Abstract: Geometric inequalities go back to antiquity, and so do their equality cases. As everyone knows, the circle is the only case when the isoperimetric inequality is sharp. But what happens to other geometric inequalities? Apparently, as the inequalities become more general, their equality cases become more cumbersome to state and even harder to prove. I will give a broad survey of various natural examples, with an emphasis on discrete inequalities. I will then explain why the celebrated Alexandrov–Fenchel inequality has intractable equality cases, what does that mean, and how this can be established. The talk is aimed at a general audience.

"Paths in Mathematics After Undergrad" Panel
2023-10-18 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Stay tuned for more details about this special event!

47 Lecture: Moon Duchin on "Rethinking Representation”
2023-10-19 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
DESCRIPTION
The Department of Mathematics and Statistics is pleased to announce the next 47 Lecture. Moon Duchin, Professor of Mathematics and Senior Fellow in the Tisch College of Civic Life at Tufts University, will give a talk titled “Rethinking Representation.” Dr. Duchin runs the MGGG Redistricting Lab, an interdisciplinary group of researchers working on the basic science of democracy. They helped commissions and state governments collect public feedback and find better redistricting maps around the country in the last cycle, and Duchin served as an expert in state and federal court cases in Wisconsin, Pennsylvania, North Carolina, South Carolina, Alabama, Georgia, and Texas.
The 47 Lecture is an annual public event sponsored by the Department of Mathematics and Statistics at Pomona College. This lecture is free and open to the Claremont Community. For more information, email the Math Department or call (909) 621-8409.

COST
This lecture is free and open to the Claremont Community.

EVENT CATEGORIES
Science/Technology and Society

EVENT CONTACT
William McGuire

CONTACT PHONE
(909) 621-8409

CONTACT EMAIL
william.mcguire@pomona.edu

CONTACT EMAIL
math@pomona.edu

CONTACT PHONE
909-621-8409

History and Philosophy of Mathematics Seminar: Louis Beaugris (Kean University)
2023-10-23 15:00 - 16:00 | Fletcher 110, Pitzer College, 1050 N Mills Ave, Claremont, CA, 91711, United States
A mathematician and all his functions: The untold story of Lucien Hibbert.
Abstract: Even with his achievements in mathematics, academia, politics, and international affairs, Lucien Hibbert is nearly unknown, even in his native land of Haiti. Our aim is to present a biography of him that includes his family ties, his education, his PhD thesis, and his work in government. His friendships with some of the most recognizable French mathematicians and how they contributed to his efforts in higher education in Haiti are also explored.

Applied Math Seminar: Evan Rosenman (CMC)
2023-10-23 16:15 - 17:15 | Estella 1021 (Emmy Noether Room), Pomona College, Claremont, CA, 91711, United States
Title: Recalibration of Predicted Probabilities Using the “Logit Shift”: Why Does It Work, and When Can It Be Expected to Work Well?
Abstract: In the context of election analysis, researchers frequently face the “recalibration problem.” That is: they must reconcile individual-level vote probabilities, modeled prior to the election, with vote totals observed in each precinct once the election has taken place. Making these adjustments such that the probabilities match known aggregates, researchers can obtain better-calibrated estimates of key quantities such as vote preferences among subgroups of the electorate defined by race, age, and gender.
We provide theoretical grounding for one of the most commonly used recalibration strategies, known colloquially as the “logit shift.” The logit shift is a heuristic adjustment, in which a constant correction on the logit scale is found, such that aggregated predictions match observed totals.
We show that the logit shift offers a fast and accurate approximation to a principled, but computationally impractical adjustment strategy: computing the posterior probabilities, conditional on the observed totals. After deriving analytical bounds on the quality of the approximation, we illustrate its accuracy using Monte Carlo simulations. We also discuss scenarios in which the logit shift is less effective at recalibrating predictions: when the totals are available only for highly heterogeneous populations, and when the original predictions correctly capture the mean of true individual probabilities, but fail to capture the shape of their distribution.

Deep hole lattices and isogenies of elliptic curves (Lenny Fukshansky, CMC)
2023-10-24 12:15 - 13:10 | Roberts North 102, CMC
For a lattice L in the plane, we define the affiliated deep hole lattice H(L) to be spanned by a shortest vector of L and the furthest removed vector from the lattice contained in the triangle with sides corresponding to the shortest basis vectors. We study the geometric and arithmetic properties of deep hole lattices, which turn out to be quite interesting. In particular, we construct sequences of deep hole lattices corresponding to elliptic curves over a fixed number field. In the case of CM elliptic curves, we prove that all elliptic curves generated by this sequence are isogenous to each other and produce bounds on the degree of isogeny. Finally, we produce a counting estimate for the planar lattices with a prescribed deep hole lattice. Joint work with Pavel Guerzhoy and Tanis Nielsen.

Claremont Topology Seminar: Wenyuan Li (USC)
2023-10-24 15:00 - 16:00 | Fletcher 110, Pitzer College, 1050 N Mills Ave, Claremont, CA, 91711, United States
Title: Generating families on Lagrangian cobordisms
Abstract: An important question in contact topology is to understand Legendrian knots and their relations given by Lagrangian cobordisms. In the contact manifold T*M x R, an important tool to study Legendrian knots and their Lagrangian cobordisms is called generating families or generating functions, which are generalizations of the defining functions f of graphical Legendrians of the form {(x, df(x), f(x))}. When there exists a generating family with good control at infinity, interesting Legendrian invariants can be extracted. We try to understand the following basic question: when can a generating function on the Legendrian knot be extended to the Lagrangian cobordism? We will give a necessary and sufficient condition to the problem for generating families with good control at infinity. In particular, we show that such an extension always exists in the case of Lagrangian concordances.

What is a moduli space? (Javier Gonzalez Anaya, HMC)
2023-10-25 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Title: What is a moduli space?
Speaker: Javier Gonzalez Anaya, Department of Mathematics, Harvey Mudd College
Abstract: A natural endeavour in mathematics is to classify objects according to their properties. For example, we can readily identify straight lines in the plane, or recognize different kinds of triangles depending on their symmetries. Less intuitive, however, is that given a class of mathematical objects, it is often possible to construct a geometric space parametrizing those objects. Known as “moduli spaces”, the study of these spaces has been a major driving force of modern geometry. In this talk we will explore some of the main ideas behind moduli theory through examples, ranging from the moduli space of lines in the plane to the one of points on the sphere. We will finish by discussing our ongoing research on the moduli space of points in d-dimensional space.

Javier González Anaya, PhD, is an algebraic geometer specializing in the study of combinatorial structures and finite generation problems within the field of birational geometry. His research extends to areas such as the theory of polytopes and machine learning. Currently, he holds a position as a visiting assistant professor at Harvey Mudd College, having previously served in a similar role at UC Riverside. Beyond his research, Javier is a committed educator and mentor, having overseen student research projects and taught an extensive range of courses.

Applied Math Seminar: Jeremy Brandman (DCS corporation)
2023-10-30 16:15 - 17:30 | Estella 1021 (Emmy Noether Room), Pomona College, Claremont, CA, 91711, United States
Title
Control algorithms for unmanned underwater vehicles: new approaches based on Hamilton-Jacobi equations and reinforcement learning.
Abstract
Unmanned underwater vehicles (UUVs) are defined by their ability to operate without direct human intervention. As a result, UUVs are valuable for surveillance tasks, especially in the presence of hazardous environmental conditions. Specific applications of UUVs include seafloor mapping, mine detection, and oil pipeline inspection.
In this talk, we propose new algorithms for two aspects of UUV control: path planning and vehicle guidance. Path planning identifies a vehicle trajectory, based on anticipated environmental conditions, that achieves desired mission objectives (e.g. obstacle avoidance, minimization of energy consumption). Vehicle guidance responds to observed environmental conditions in order to maintain fidelity to the path selected by the path planner.
The first half of this talk considers a new approach to path planning based on solving Hamilton-Jacobi partial differential equations (PDE). The starting point for this method is the observation that the vehicle’s minimum travel-time satisfies a time-independent Hamilton-Jacobi equation . Numerical solutions to this PDE are efficiently computed using the fast sweeping method. Our approach is validated through several examples for which optimal trajectories are derived using the calculus of variations.
The second half of this talk introduces a reinforcement learning framework for incorporating in situ ocean current measurements into the guidance system in an energetically optimal manner. Scaling and symmetry considerations turn out to play an important role in the framework’s efficiency and robustness. Numerical results demonstrate that the energetic cost of transits executed under the guidance of a trained agent approaches optimal performance.

On the spectra of syntactic structures (Isabella Senturia, Yale University)
2023-10-31 12:15 - 13:10 | On Zoom
We explore the application of spectral graph theory to the problem of characterizing linguistically-significant classes of tree structures. We focus on various classes of syntactically-defined tree graphs, and show that the spectral properties of different matrix representations of these classes of trees provide insight into the linguistic properties that characterize these classes. More generally, our goal is to provide another route to understanding the mathematical structure of natural language, one that does not come from extensive definitions and rules defined via linguistic extrapolation, but instead is extracted directly from computation on the syntactically-defined graphical structures.

Claremont Topology Seminar: Konstantinos Varvarezos (UCLA)
2023-10-31 15:00 - 16:00 | Fletcher 110, Pitzer College, 1050 N Mills Ave, Claremont, CA, 91711, United States
Title: Cosmetic Surgeries on Knots and Heegaard Floer Homology
Abstract: A common method of constructing 3-manifolds is via Dehn surgery on knots. A pair of surgeries on a knot is called purely cosmetic if the resulting 3-manifolds are homeomorphic as oriented manifolds, whereas it is said to be chirally cosmetic if they result in homeomorphic manifolds with opposite orientations. An outstanding conjecture predicts that no nontrivial knots admit any purely cosmetic surgeries. We apply certain obstructions from Heegaard Floer homology to show that (nontrivial) knots which arise as the closure of a 3-stranded braid do not admit any purely cosmetic surgeries. Furthermore, we find new obstructions to the existence of chirally cosmetic surgeries coming from Heegaard Floer homology; in particular, we make use of immersed curve formulations of knot Floer homology and the corresponding surgery formula. Combining these with other obstructions involving finite type invariants, we completely classify chirally cosmetic surgeries on odd alternating pretzel knots. Moreover, we rule out cosmetic surgeries for L-space knots along slopes with opposite signs.

Slope Gap Distributions of Translation Surfaces (Taylor McAdam, Pomona College)
2023-11-01 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Title: Slope gap distributions of translation surfaces
Speaker: Taylor McAdam, Department of Mathematics, Pomona College
Abstract: How “random” are the rational numbers? To make sense of this question, let us consider the set of Farey fractions of level n—that is, the rational numbers between 0 and 1 with denominator at most n. It turns out that these distribute uniformly in the unit interval as n goes to infinity, which would suggest they appear to be quite random. However, we may consider a finer test of randomness by considering the distribution of gaps between consecutive Farey fractions as n tends to infinity. To investigate this, we will first realize the Farey fractions as the slopes of geodesic paths on the (square) flat torus—a geometric object obtained by gluing the opposite edges of a square together. We will then define the horocycle flow on the space of all flat tori, which will allow us to study our question about gaps between Farey fractions via a dynamical system. Finally, we will see how this method can be generalized to study the slope gap distributions for paths on a larger class of geometric objects called translation surfaces and discuss results on the collection of surfaces obtained by gluing together opposite edges of the regular 2n-gon.

Taylor McAdam graduated with a Bachelor’s degree in mathematics from Harvey Mudd College in 2013 before starting a doctoral program at University of Texas at Austin. In 2017, she transferred to the University of California San Diego, where she received her PhD in mathematics in 2019 under the supervision of Amir Mohammadi. She was an NSF Postdoctoral Fellow at Yale University from 2019 to 2023, before joining the faculty at Pomona College in 2023 as a Visiting Assistant Professor. Her research interests lie at the intersection of dynamical systems, geometry, and number theory, and she is passionate about undergraduate math education and building inclusive mathematical communities.

GEMS November 4th Session
2023-11-04 10:00 - 12:00 | Shanahan 1480, Harvey Mudd College, 301 Platt Blvd., Claremont, CA, 91711, United States

Applied Math Seminar: Claremont Colleges Course Previews for Spring 2024
2023-11-06 16:15 - 17:15 | Estella 1021 (Emmy Noether Room), Pomona College, Claremont, CA, 91711, United States
During this student-centered Applied Math Seminar, there will be discussion and presentations about upcoming courses offered in applied mathematics, to help students make their enrollment choices for Spring 2024 and beyond.

Frobenius coin-exchange generating functions (Matthias Beck, San Francisco State University)
2023-11-07 12:15 - 13:10 | Roberts North 102, CMC
We study variants of the Frobenius coin-exchange problem: Given n positive relatively prime parameters, what is the largest integer that cannot be represented as a nonnegative integral linear combination of the given integers? This problem and its siblings can be understood through generating functions with 0/1 coefficients according to whether or not an integer is representable. In the 2-parameter case, this generating function has an elegant closed form, from which many corollaries follow, including a formula for the Frobenius problem. We establish a similar closed form for the generating function indicating all integers with exactly k representations, with similar wide-ranging corollaries. This is joint work with Leonardo Bardomero.

Claremont Topology Seminar: Hyunki Min (UCLA)
2023-11-07 15:00 - 16:00 | Fletcher 110, Pitzer College, 1050 N Mills Ave, Claremont, CA, 91711, United States
Title: Contact structures and the mapping class group of lens spaces
Abstract: One important problem in contact topology is to classify contact structures on a given manifold. Around 20 years ago, Giroux and Honda classified contact structures on lens spaces. A natural question to ask after that is how the transformations on lens spaces interact with the contact structures. In this talk, we study contactomorphisms on lens spaces, which are diffeomorphisms preserving the contact structure. We show that the contact mapping class group of a standard contact lens space is a subgroup of the mapping class group of the lens space.

Lonely Runners and My Favorite Polyhedron (Matthias Beck, San Francisco State University)
2023-11-08 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Title: Lonely Runners and My Favorite Polyhedron
Speaker: Matthias Beck, Department of Mathematics, San Francisco State University
Abstract: We study the Lonely Runner Conjecture, conceived by Wills in the 1960’s, and originally phrased in terms of Diophantine approximation: Given positive integers n_1, n_2, …, n_k, there exists a positive real number t such that for all 1 ≤ j ≤ k the distance of t n_j to the nearest integer is at least 1/(k+1). This conjecture can be recast in lay terms: if k runners with different (constant) speeds move around a circular track of length 1, then for each runner there will be a time when they have distance at least 1/k to the others. This (in)famous conjecture in combinatorial number theory is open for k ≥ 7.We will give a brief history of the Lonely Runner Conjecture and some of its variants, emphasizing a view-obstruction approach by Cusick and recent work by Henze and Malikiosis; our goal is to promote a polyhedral ansatz to the Lonely Runner Conjecture. Our results include affirmative instances that become (quite literally) visible through polyhedral geometry.
Based on joint work with Serkan Hosten (SF State) and Matthias Schymura (Rostock).

Matthias Beck is a professor of mathematics at San Francisco State University and has had visiting positions at SUNY Binghamton, the Mathematical Sciences Research Institute in Berkeley, the Max-Planck-Institute in Bonn, Cornell University, Vassar College, and the Freie Universität in Berlin. Matt’s research is in combinatorics and number theory, in particular, counting integer points in polyhedra and the application of these enumeration functions to various mathematical topics and problems. He (co-)authored four books and numerous research papers, many of which feature student coauthors. Matt was honored with the Mathematical Association of America’s Haimo Award for Distinguished College or University Teaching of Mathematics in 2013.x`

Applied Math Seminar: Adam Yassine (Pomona College)
2023-11-13 04:15 - 17:15 | Estella 1021 (Emmy Noether Room), Pomona College, Claremont, CA, 91711, United States
Title: On the Composition of Classical Mechanical Systems
Abstract: Compositionality is a basic principle for understanding the physical world. The underlying idea is to study a system by studying the ways in which the components of the system compose to form the system. Category theory is an area in mathematics that is particularly well-suited for studying questions about compositionality. This talk will outline a way to use category theory to study classical mechanical systems from a compositional perspective.

History and Philosophy of Mathematics Seminar: Kris Palmieri (University of Chicago)
2023-11-13 15:00 - 16:00 | Fletcher 110, Pitzer College, 1050 N Mills Ave, Claremont, CA, 91711, United States
True Grit: Writing the History of Women at Yerkes Observatory, 1895–1950
Abstract:
Women at Yerkes Observatory earned advanced degrees, conducted their own research, collaborated on projects with peers of both sexes, and authored publications in their own names in the first half of the Twentieth Century. Yet Alice Hall Farnsworth, Mary Murray Hopkins, Harriet McWilliams Parsons, and Evelyn Worhnam Wickham – to name only a few – are unknown even amongst specialists. This is in large part because their lives and their labor are all but invisible in published sources and public records. Yet the voices of these women remain preserved in archives across the country – and this presents us with an unparalleled opportunity to reconstruct their lived experiences as women in science.
This paper explores the ways in which biography provides a uniquely productive lens for reconstructing the history of women at Yerkes. In so doing, however, it also explores the limits of biography for a research project that is anchored by its focus on a specific institutional space and asks how these limits might be overcome.

f^*-vectors of lattice polytopes (Max Hlavacek, Pomona College)
2023-11-14 12:15 - 13:10 | Roberts North 102, CMC
The Ehrhart polynomial of a lattice polytope P counts the number of integer points in the nth integral dilate of P. The f^* -vector of P, introduced by Felix Breuer in 2012, is the vector of coefficients of the Ehrhart polynomial with respect to the binomial coefficient basis . Similarly to h and h^* -vectors, the f^* -vector of P coincides with the f-vector (counting faces of every dimension) of its unimodular triangulations (if they exist). We give several inequalities that hold among the coefficients of f^*-vectors of polytopes. These inequalities resemble striking similarities with existing inequalities for the coefficients of f-vectors of simplicial polytopes. Even though f^* -vectors of polytopes are not always unimodal, we describe several families of polytopes that carry the unimodality property.

Geometry and Topology Seminar: Claremont Colleges Course Previews for Spring 2024
2023-11-14 15:00 - 16:00 | Fletcher 110, Pitzer College, 1050 N Mills Ave, Claremont, CA, 91711, United States
On November 14th, Tuesday from 3-4pm in Fletcher 110, Geometry and Topology Seminar invites students and faculty to a course preview session devoted to a discussion and presentations about upcoming Spring 2024 courses in

geometry,
topology and/or
with applications in geometry and topology

to help students make their enrollment choices.
We will have some refreshments for all attending to enjoy!

Adinkra Heights and Color-Splitting Rainbows (Ursula Whitcher, American Mathematical Society)
2023-11-15 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Title: Adinkra Heights and Color-Splitting Rainbows
Speaker: Ursula Whitcher, American Mathematical Society
Abstract: Adinkras are decorated graphs that encapsulate information about conjectural relationships between fundamental particles in physics. If we color the edges of an Adinkra with a rainbow of shades in a specific order, we obtain a special curve that we can study usingalgebraic and geometric techniques. We use this structure to characterize height functions on Adinkras, then show how to compute the same information using data from our rainbow. This talk describes joint work with Amanda Francis.

Dr. Ursula Whitcher is an associate editor at Math Reviews (MathSciNet), a project of the American Mathematical Society, covering a range of areas from algebraic geometry to history of mathematics. Before joining the AMS, Dr. Whitcher earned a PhD from the University of Washington, was a Teaching and Research Postdoctoral Fellow at Harvey Mudd, and became an associate professor at the University of Wisconsin-Eau Claire. Find Dr. Whitcher’s mathematically inspired poetry and fiction in Asimov’s Science Fiction Magazine, Analog, or the Journal of Humanistic Mathematics.
