The seminar meets on Mondays, from 4:10 to 5 p.m. (Pacific time) in WEBS 11. Please email Sheng-Chi Liu (shengchi.liu@wsu.edu) if you would like to give a talk.
Spring 2025 Schedule
| Date | Speaker | Title and Abstract |
| January 6 | Organizational Meeting | |
| January 13 | Sheng-Chi Liu | Title: Weyl sums and equidistributions in number theory Abstract: This is an introductory talk on Weyl sums and certain equidistribution problems in number theory. |
| January 20 | No Seminar (University Holiday) | |
| January 27 | Feng-Hao Liu (Washington State University) | Title: Fully Homomorphic Encryption in Polynomial Modulus – New Developments and Applications Abstract: Fully Homomorphic Encryption (FHE) is a powerful technology that enables computations on encrypted data without requiring decryption. This capability is especially valuable for private outsourced computation, where a user can upload their encrypted input to a server. The server in turn, can compute and return for any arbitrary function (e.g., a classifier function), without accessing the private data . This process allows the user to learn the result without exposing to the server, thereby achieving private outsourced computation as a service. In recent years, machine learning (ML) functions, such as decision trees and MNIST/CIFAR-10 inference functions, have been extensively studied in this context. Despite its theoretical potential, implementing FHE computations in practice – such as solving the encrypted inference problem in real-time – remains a significant challenge. Recent research has focused on bridging the gap between theory and practical application. In this work, we explore recent advancements in the third generation of FHE schemes (e.g., GSW, FHEW/TFHE), which rely on milder lattice assumptions (i.e., a polynomial modulus-to-noise ratio) and offer smaller key sizes and reduced memory usage. We present novel algebraic techniques that achieve non-trivial SIMD bootstrapping for this generation for the first time. Additionally, we discuss advances in hardware acceleration and practical deployment in ML, particularly for inferences in MNIST and CIFAR-10. We hope that our techniques will contribute to further improvements in both theoretical and practical aspects of FHE. |
| February 3 | Shuai Zhai (Shandong University) Meet on Zoom | Title: BSD conjecture and Goldfeld’s conjecture Abstract: It is widely recognized that there is a deep connection between the analytical and algebraic aspects of elliptic curves, namely the Birch and Swinnerton-Dyer conjecture, which is one of the Millennium Prize Problems. In this presentation, I will start with some classical equations to provide an overview of the arithmetic of elliptic curves. I will then present some results related to the BSD conjecture and Goldfeld’s conjecture. |
| February 10 | Yingnan Wang (Shenzhen University) Meet on Zoom | Title: On the first sign change of Fourier coefficients of cusp forms Abstract: In the talk, we will survey some recent progress on the first sign change of Fourier coefficients of cusp forms and present a variant of the current widely used method initiated by Choie and Kohnen in the study of the location of the first sign change of the Fourier coefficients of a holomorphic cusp form when all the coefficients are real. This variant of Choie and Kohnen`s method applies to more cases including integral weight cusp forms on congruence subgroups of any levels as well as half-integral weight cusp forms. This is a joint work with Guohua Chen and Yuk-Kam Lau. |
| February 17 | No Seminar (University Holiday) | |
| February 24 | Daryl DeFord | Title: Generalized Lucas Sequences and Enumerating Distinct Chessboard Tilings Abstract: In this talk I will discuss enumeration results about tiling problems, including recurrences and bounds for tilings with squares, enumerating tilings up to symmetry, and impossibility results for expressing certain tilings problems as perfect matchings. If there is time I will also discuss applications of these techniques to constructing higher-order Lucas sequences. |
| March 3 | Amber Thrall | Title: Steinhaus Filtration and Stable Paths in the Mapper Abstract: In this talk I will define a new filtration called the Steinhaus filtration built from a single cover based on a generalized Steinhaus distance, a generalization of Jaccard distance. We will also show that the Steinhaus filtration is stable given a finite cover. Finally, we will apply the Steinhaus filtration to determine stable paths in the Mapper graph with applications in recommendation systems. As an example, we will determine which sequence of movies provides a gentle transition from one movie to another. |
| March 10 | No Seminar (Spring Vacation) | |
| March 17 | Matthew Hudelson | Title: Recurrences of Fringed Rectangle Tilings and an Affirmative Answer to Daryl’s Symmetry Conjecture Abstract: In an earlier talk, Daryl Deford posited the following conjecture concerning tilings of rectangles with dominos: Fix a positive integer k. Let a_n be the number of ways to tile a k x n rectangle with dominos. We claim that the sequence A = a_1, a_2, a_3, … obeys a linear recurrence that, if used to extend the sequence to non-positive indices and then shifted by one position results in an extended sequence B = …, b_(-2), b_(-1), b_0, b_1, b_2,… where |b_(-n)| = b_n for all non-negative integers n. We will show that this conjecture is in fact true for all positive integers k. |
| March 24 | No Seminar | |
| March 31 | Jared Brannan | Title: Young Tableaux and Generalizations Abstract: Young Tableaux are Young Diagrams (left and top justified pieces of the square grid) which are populated with partitions of $n$ so that each part is less than or equal to the part to the right and strictly less than the part below. In this talk we apply methods from the theory of Young Tableaux to analogous problems on trees. |
| April 7 | Garrett Kepler | Title: A Probabilistic Excursion in Spectral Graph Theory Abstract: In this talk, we will explore the mutually beneficial relationship between probability theory and spectral graph theory. At their intersection lie lots of perplexing puzzles and fresh features. Through ample example, we will showcase their established significant symbiotic synergy. Moreover, we will meander through many musings and mysteries. |
| April 14 | Benjamin Clark | Title: An experimental approach to the S-SNIEP using algebraic geometry Abstract: The stochastic symmetric nonnegative inverse eigenvalue problem (S-SNIEP) asks for the necessary and sufficient conditions for a list of real numbers to be the spectra of a stochastic symmetric nonnegative matrix. Using tools from algebraic geometry, it is shown that the S-SNIEP is solvable by polynomial inequalities and the reality condition. An experimental approach is then presented for forming the desired feasibility region of the S-SNIEP for small matrices. This approach is then used to generate a conjectured solution to the n=4 case. We conclude by giving short comings to this approach and potential future ideas. |
| April 21 | Tea | Please join us for the end-of-semester tea at the Hacker Lounge. |