Abstracts
Speaker : 송용수
Title : Evolution of Cryptography: From Foundational Concepts to Modern Innovations
Abstract : The evolution of cryptography showcases a remarkable journey from foundational principles to modern-day innovations. This presentation delves into pivotal milestones, beginning with seminal concepts such as semantic security and the advent of probabilistic encryption by Goldwasser and Micali. Tracing the historical progression, it explores the groundbreaking contributions of symmetric and public-key cryptography, featuring prominent algorithms like AES, Diffie-Hellman key-exchange, Elgamal and RSA encryptions. Transitioning from theory to contemporary trends, the discussion illuminates recent advancements like zero-knowledge proofs and secure multi-party computation, elucidating their significance in enhancing privacy and security in a digitally connected world. This abstract encapsulates a comprehensive narrative, showcasing cryptography's transformative journey from its theoretical underpinnings to its cutting-edge applications and emerging frontiers.
Speaker : 오정석 (Talk 1) [slides]
Title : The quantum Lefschetz principle
Abstract : “Quantum Lefschetz” is a pretentious name for understanding how moduli spaces -- and their virtual cycles and associated invariants -- change when we apply certain constraints. (The original application is to genus 0 curves in P^4 when we impose the constraint that they lie in the quintic 3-fold.) When it doesn’t work there are fixes (like the p-fields of Guffin-Sharpe-Witten/Chang-Li) for special cases associated with curve-counting. We will describe joint work with Richard Thomas developing a general theory.
Speaker : 김명호 [slides]
Title : 클러스터대수와 표현론
Abstract : 클러스터 대수는 변이(mutation)라고 불리는 작용을 반복하여 얻은 클러스터 변수(cluster variable)들로 생성되는 유리함수체의 부분환으로서, 다양한 분야에서 나타나는 중요한 대수적 구조입니다 이 강연에서는 클러스터대수의 기본적인 내용을 소개하고, 표현론에서 나타나는 예제들을 살펴보겠습니다.
Speaker : 오정석 (Talk 2) [slides]
Title : The quantum Lefschetz principle
Abstract : “Quantum Lefschetz” is a pretentious name for understanding how moduli spaces -- and their virtual cycles and associated invariants -- change when we apply certain constraints. (The original application is to genus 0 curves in P^4 when we impose the constraint that they lie in the quintic 3-fold.) When it doesn’t work there are fixes (like the p-fields of Guffin-Sharpe-Witten/Chang-Li) for special cases associated with curve-counting. We will describe joint work with Richard Thomas developing a general theory.
Speaker : Valentin Buciumas [slides]
Title : Hecke algebras, Whittaker functions and quantum groups
Abstract : I will give a brief overview of the Satake isomorphism and the Casselman-Shalika formula, which are basic tools in the representation theory of p-adic groups. These two results essentially state that the spherical Hecke algebra and the spherical Whittaker functions on a p-adic group can be understood in terms of the representation theory of the dual group. When passing from p-adic groups to their metaplectic covers, it was conjectured by Gaitsgory and Lurie (recently proved in different settings by Campbell-Dhillon-Raskin and Buciumas-Patnaik) that the dual group gets replaced by a certain quantum group at a root of unity. I will try to explain the conjecture of Gaitsgory-Lurie and if time permits some of the ideas of the proof.