Views 1494 Votes 0 Comment 0
?

Shortcut

PrevPrev Article

NextNext Article

Larger Font Smaller Font Up Down Go comment Print
?

Shortcut

PrevPrev Article

NextNext Article

Larger Font Smaller Font Up Down Go comment Print
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
No. Subject Author Date Views
Notice QSMS Mailing List Registration qsms 2021.09.09 4796
125 [SNU Number Theory Seminar 14 Apr] Homological interpretation of Hecke $L$-values over real quadratic fields qsms 2023.03.31 1140
124 [QSMS Symplectic topology seminar-20230828] From Babylonian lunar observations to global surfaces of section qsms 2023.08.21 1141
123 [QSMS-BK21 Symplectic Seminar 26 May] 1. Product structures on the relative symplectic cohomology 2. Symplectic homology of affine varieties qsms 2023.05.25 1142
122 [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 1142
121 [QSMS Monthly Seminar 2023-04-21] Lagrangian submanifolds and their Legendrian lifts qsms 2023.04.21 1151
120 [QSMS Geometry seminar 2023-05-25] Symplectic field theory and codimension-2 stable Hamiltonian submanifolds qsms 2023.05.25 1164
119 [QSMS Geometry Seminar 20221230] Morphism spaces between coisotropic A-branes qsms 2022.12.27 1166
118 [QSMS Symplectic topology seminar 20230817] Symplectic Torelli classes of positive entropy qsms 2023.08.14 1169
117 [QSMS-BK21 Symplectic Seminar 28 Apr] PGL(2,Q_p)-ORBIT CLOSURES ON A p-ADIC HOMOGENEOUS SPACE OF INFINITE VOLUME qsms 2023.05.12 1173
116 [QSMS Monthly Seminar 2023-03-24] Rational points on abelian varieties qsms 2023.03.24 1176
115 [QSMS-BK21 Symplectic Seminar 12 May] Introduction to Floer Homotopy: Global Kuranishi Charts via Abouzaid-McLean-Smith qsms 2023.05.12 1181
114 [QSMS-BK21 Symplectic Seminar 30 June] Matrix Factorizations qsms 2023.06.26 1182
113 [SNU Number Theory Seminar 2 June] A refined Tamagawa number conjecture for modular forms qsms 2023.04.20 1186
112 [QSMS Seminar 2022-10-25] Rational liftings and gRSK qsms 2022.10.08 1192
111 [QSMS-BK21 Symplectic Seminar 14 July] Introduction to 3D Mirror Symmetry, from a Symplectic Viewpoint / Orbifolding Lagrangian Floer Cohomology qsms 2023.07.12 1196
110 [QSMS Seminar 2022-09-27] Categories of Whittaker Modules over Lie superalgebras and Categorification of Fock Spaces qsms 2022.09.20 1213
109 [QSMS Seminar 2022-12-2] N=2 supersymmetric W algebras from Hamiltonian reduction qsms 2022.11.25 1228
108 [2022 Global KMS International Conference 10/19 ~ 10/21] Related talks qsms 2023.01.05 1229
107 [QSMS-BK21 Symplectic Seminar 10 Mar] Mirror Symmetry for Log Calabi-Yau Surfaces qsms 2023.03.09 1240
106 [QSMS Monthly Seminar 2022-10-28] Oscillator representations of quantum affine algebras   qsms 2022.10.30 1244
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8