조회 수 3106 추천 수 0 댓글 0
?

단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
?

단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
Extra Form
일정시작 2022-07-18
일정종료 2022-07-19
배경색상 #7164D0
반복주기 1
반복단위 1.일(단위)

Speaker :  Pablo Portilla cuadrado (University of Lille)
Place :  상산관 129동 406호
Schedule :  7/11  (Mon)  Survival kit on plane curve singularities I
                    7/12  (Tue)   Survival kit on plane curve singularities II

                    7/18  (Mon)  Characterizing the geometric monodromy group of an isolated plane curve singularity

                    7/19  (Tue)  A quadratic form associated with pseudo-periodic homeomorphisms arising from singularity theory

                    (each day)   10:30 ~ 11:30,   11:45 ~ 12:45

 

TiTle :  Survival kit on plane curve singularities I & II

Abstract : 

The study of plane curve singularities is one of the most classical parts of singularity theory going back to Newton in the XVII century. When one studies complex polynomials in two variables, singularities appear in a very natural way. Although many times this topic is treated from an algebraic point of view, one quickly sees that it has many ties with low dimensional topology
topics such as knot theory and mapping class groups.

In this mini-course we will make a gentle introduction to singularity theory through the world of plane curves. We will focus on the topological aspect of singularities and we will mainly learn techniques through rich examples. By the end of the course we will be able to compute many invariants of a plane curve singularity and we will understand the topology around a singular point of an algebraic plane curve. In particular we will learn how to find parametrizations of each irreducible component of a plane curve singularity. We will see how these parametrizations can result very useful in computing the embedded topology of each branch and how each branch interacts with the rest. We will learn to find smooth models (resolve) of  plane curve singularities by repeatedly blowing up the ambient space and, from the final picture, we will understand the topology of the Milnor fibration and its geometric monodromy. We will end the course by introducing the versal unfolding of a plane curve singularity and posing some questions that naturally emanate from it.

Title :  Characterizing the geometric monodromy group of an isolated plane curve singularity

Abstract :

In this talk we will explain an intrinsic characterisation of the geometric monodromy group of an isolated plane curve singularity as the stabiliser in the mapping class group of the Milnor fiber of the relative isotopy class of a canonical vector field. We will also discuss two interesting consequences of this result: an easy and efficient criterion for detecting whether a simple closed curve in the Milnor fiber is a geometric vanishing cycle or not, and the non-injectivity of the natural representation of the versal unfolding of the singularity. This is a joint work with Nick Salter.

 

Title :  A quadratic form associated with pseudo-periodic homeomorphisms arising from singularity theory
Abstract :

In this talk, we study the nilpotent part of a pseudo-periodic automorphism of a real oriented surface with boundary. We associate a quadratic form Q defined on the first homology group of the surface. Using some techniques from mapping class group theory, we prove that a related form  is positive definite under some conditions that are always satisfied for monodromies of Milnor fibers of germs of curves on normal surface singularities. Moreover, the form Q is computable in terms of the dual resolution or semistable reduction graph. Numerical invariants associated with Q are able to distinguish plane curve singularities with different topological types but same spectral pairs. This is a joint work with L. Alanís, E. Artal, C. Bonatti, X. Gómez-Mont and M. González Villa.

 

 

 


List of Articles
번호 제목 글쓴이 날짜 조회 수
공지 QSMS Mailing List Registration qsms 2021.09.09 12034
88 [QSMS Seminar 2023-10-06, 11-03] Algebraic group analogues of the Slodowy slices and the structure of the set of conjugacy classes in algebraic groups / Poisson q-W-algebras qsms 2023.09.11 3385
87 [QSMS Seminar 2023-12-13] A user’s guide to Schubert calculus of Lagrangian Grassmannians qsms 2023.11.27 3272
86 [QSMS Symplectic geometry seminar 2023-10-17, 18] New approaches to discovering symplectic non-convexity / Banach-Mazur distances in symplectic and contact geometry qsms 2023.10.10 3175
85 [QSMS Symplectic geometry seminar 2023-10-24] Linear bounds on rho-invariants and simplicial complexity of manifolds qsms 2023.10.24 3355
84 [QSMS Symplectic topology seminar 20230811, 0817] Spectral numbers in Tate Rabinowitz Floer Homology qsms 2023.08.04 3353
83 [QSMS Symplectic topology seminar 20230817] Symplectic Torelli classes of positive entropy qsms 2023.08.14 3329
82 [QSMS Symplectic topology seminar-20230828] From Babylonian lunar observations to global surfaces of section qsms 2023.08.21 3389
81 [QSMS Symplectic topology seminar-20240507]  Introduction to triangulated persistence categories qsms 2024.05.10 20
80 [QSMS Symplectic topology seminar-20240514] Computing Fukaya categories: Techniques and Examples qsms 2024.05.10 38
79 [QSMS 기하/위상 세미나 2021.09.06] The mirror P=W conjecture from homological mirror symmetry of Fano manifolds qsms 2021.09.03 3440
78 [QSMS 위상기하 세미나 2021.11.25] Exotic families of Weinstein manifolds with Milnor fibers of ADE types qsms 2021.11.19 3294
77 [QSMS 집중강연 Representation theory 2023-02-07] Mini-course on quantum symmetric pairs I qsms 2023.01.03 3005
76 [QSMS 집중강연 Representation theory 2023-02-13] Mini-course on quantum symmetric pairs II qsms 2023.01.05 3135
75 [QSMS-BK21 Seminar 2022-08-29] Symplectic Cohomology, String Topology, and Deformations qsms 2022.08.29 2982
74 [QSMS-BK21 Seminar] Past seminars qsms 2022.08.26 3020
73 [QSMS-BK21 Symplectic Geometry Seminar 2022-09-30] Introduction to Floer Homotopy: Bordism and Flow Categories qsms 2022.09.26 2996
72 [QSMS-BK21 Symplectic Geometry Seminar 2022-11-04] Introduction to Floer Homotopy: Kuranishi Structures qsms 2022.10.26 2989
71 [QSMS-BK21 Symplectic Geometry Seminar 2022-12-09] Introduction to Floer Homotopy: Formal Groups and Complex Cobordism qsms 2022.11.28 2977
70 [QSMS-BK21 symplectic semiar] Part 4 (23' Aug 18 ~) qsms 2023.12.27 2984
69 [QSMS-BK21 Symplectic Seminar 10 Mar] Mirror Symmetry for Log Calabi-Yau Surfaces qsms 2023.03.09 2992
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8