Prev. week | Oct 19–25, 2025 | Next week
Sunday,
October 19 |
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Monday,
October 20 |
- 15:30–16:30 Algebra and Number Theory Seminar, Kemeny 343
 
- The distribution of 2-Selmer groups in quadratic twist families
- Ariel Weiss, Trinity College
- The Poonen–Rains and Bhargava–Kane–Lenstra–Poonen–Rains give striking predictions for the distribution of Selmer groups in the family of all elliptic curves over $\mathbb{Q}$. In particular, they predict that the average size of the $p$-Selmer group is $1+p$, a result proved for $p=2,3,5$ by Bhargava and Shankar.
However, these models do not accurately describe families of elliptic curves with isogenies, where the average $p$-Selmer size can even be infinite. In this talk, I will report on work in progress to determine the distribution of $2$-Selmer groups in the family of quadratic twists of an elliptic curve with a $2$-torsion point. I will present a theorem that shows that the distribution of the $2$-Selmer groups coincides with a distribution arising from the kernels of random matrices. This work is joint with Harald Helfgott, Zev Klagsbrun, and Jennifer Park.
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Tuesday,
October 21 |
- 11:00–12:00 Combinatorics Seminar, Kemeny 307
- Three (surprising) conjectures on pattern avoidance
- Stoyan Dimitrov, Dartmouth College
- Three independent conjectures supported by computational evidence, all related to pattern avoidance in permutations, will be discussed. The first one is about avoidance of permutation patterns with required gaps between the letters. The second, if true, will relate the well-known In-shuffles and Monge shuffling methods, when one uses these methods to sort permutations. The last surprise we have is a conjecture on the density (and thus the count) of permutations with a single cycle avoiding a pattern. Some related results (not only conjectures) will be also discussed on the way.
- 15:30–16:30 Functional Analysis Seminar, Kemeny 343
- Generalized Filtrations of Banach and Fredholm Manifolds
- Jody Trout, Dartmouth College
- Poster
- 17:30–18:30 Undergraduate Math Society Talk, Kemeny 006
- tbd
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Wednesday,
October 22 |
- 19:00–20:00 SIAM Chapter Event, Kemeny 307
- Math Alumni Panel
- Special privilege of hearing from four Dartmouth Alumni who walked down the math major path to end up at top companies!
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Thursday,
October 23 |
- 15:15 Math Colloquium, Kemeny 007
- Political Geometries: Analyzing Fairness in Redistricting with Mathematics
- Daryl DeFord, Vassar College
- The problems of constructing "fair" political districts and detecting intentional gerrymandering have received a significant amount of attention in recent years. Quantitative measures of partisan symmetry are often combined with thresholds or ensemble sampling methods to determine whether a districting plan is sufficiently "unfair" to require intervention. In this talk I will discuss the mathematical analysis of partisan symmetry measures and their (unintended) consequences, including characterization theorems, which is particularly relevant in the context of a bill passed earlier this month in Utah. I will also introduce some new Markov chains for creating ensembles of districting plans. These techniques have also helped inform legislative reform efforts, support line-drawing commissions, and provide evidence in court challenges, including cases at the Supreme Court, and I will discuss what it is like to translate mathematical and statistical research to these applied settings, as well as some of the related data, computational, and communication challenges. This talk will be accessible to undergraduates.
- Poster
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Friday,
October 24 |
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Saturday,
October 25 |
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Prev. week | October 19–25, 2025 | Next week
