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Sunday,
September 28 |
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Monday,
September 29 |
- 15:30 Algebra and Number Theory Seminar, Kemeny 343
 
- Unbounded average Selmer ranks in torsion families
- Tristan Phillips, Dartmouth College
- In their groundbreaking work, Bhargava and Shankar established the first unconditional bounds on the average rank of elliptic curves over the rational numbers by bounding the average sizes of their 2-Selmer groups—and subsequently the 3-, 4-, and 5-Selmer groups. In contrast, Klagsbrun and Lemke Oliver demonstrated that the average size of the 2-Selmer
group becomes unbounded when restricting to elliptic curves over Q with a rational 2-torsion point. This talk presents a generalization of their result to broader settings, including elliptic curves with more general torsion subgroups and defined over arbitrary number fields.
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Tuesday,
September 30 |
- 11:00–12:00 Combinatorics Seminar, Kemeny 307
- On the e-positivity of chromatic symmetric functions
- Foster Tom, Dartmouth College
- We describe how the chromatic symmetric function of two graphs glued at a single vertex can be expressed as a matrix multiplication using certain information of the two individual graphs. We then prove new e-positivity results by using a connection between forest triples and Hikita's probabilities associated to standard Young tableaux. We also prove new non-e-positivity results by considering connected partitions of our graph.
- 15:30 Functional Analysis Seminar, Kemeny 434
- Phaseless Sampling on ρ-th root lattices
- Shuang Guan, Tufts University
- We investigate uniqueness sets on the real line for L^2 functions whose Fourier transforms exhibit super-exponential decay. Such functions can be analytically extended to entire functions of a specified order ρ>1. We establish two results concerning the density of their zeros. This theoretical framework generalizes existing results for the 2nd order case (ρ=2) to any order ρ>1. Finally, we apply these findings to the Short-Time Fourier Transform (STFT) phase retrieval problem, demonstrating that if the window function belongs to this class, uniqueness of a signal can be guaranteed from its STFT intensity measurements on a sufficiently dense ρ-root lattice.
- Poster
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Wednesday,
October 1 |
- 16:00 Undergraduate Math Society Talk, Kemeny 105
- Introduction to Proofs
- Dartmouth Math Society
- Learn about proofs, mathematical logic, set theory, and the concept of infinity.
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Thursday,
October 2 |
- 15:15 Math Colloquium, Kemeny 007
- Different Differences
- Ron Buckmire, Marist University
- From Calculus we know that a derivative of a function can be approximated using a difference quotient. There are different forms of the difference quotient, such as the forward difference (most common), backward difference (less common) and centered difference (more accurate). In this talk I will discuss several different differences, specifically nonstandard finite differences (NSFD) that can be used to approximate the derivatives that appear in differential equations as a solution technique. Many NSFD schemes have been created, discovered, and promoted by Dr. Ronald E. Mickens, an African American Emeritus Professor of Physics at Clark Atlanta University, who has written more than 300 research articles and a dozen books. I'll provide examples of NSFD schemes that can be used to solve a wide variety of problems drawn from several different topics such as first-semester Calculus, elementary ordinary differential equations, and more advanced differential equations.
- Poster
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Friday,
October 3 |
- 18:00 ∿ Lahr Lecture ∿, Kemeny 008
- Squaring the Rainbow: The Intersection of LGBT and Mathematics is NOT Empty
- Ron Buckmire, Marist University
- In this talk I will discuss the ways that LGBT identity and mathematics intersect professionally, historically, and personally. Professionally, I will discuss how LGBT identity can and does impact participation in mathematics. Historically, I will provide examples that demonstrate the intersection of LGBT identity and mathematics is non-empty in the past, present and future. Personally, I will describe how my career trajectory in mathematics has (and has not) been affected by my identities as a Black gay immigrant.
NOTE: this talk requires almost no prior mathematical knowledge (not that there’s anything wrong with that!)
- Poster
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Saturday,
October 4 |
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Prev. week | September 28 – October 4, 2025 | Next week
