Views 1495 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 4798
145 weekplan_672_2020 secret qsms 2020.11.18 0
144 [QSMS Monthly Seminar 2024-03-22] Lifting problem for universal quadratic forms / Poincare duality in Rabinowitz Floer homology qsms 2024.03.22 414
143 [SNU Topology seminar 2024-03-20] Topology of singularities of complex hypersurfaces / The monodromy conjecture for simplicial nondegenerate singularities qsms 2024.03.05 673
142 [QSMS Representation theory seminar 2024-03-29] Quantum Grothendieck rings of Hernandez-Leclerc Categories qsms 2024.03.05 734
141 [QSMS Representation theory seminar 2024-01-31] Kostant’s problem for Whittaker modules over Lie superalgebras qsms 2024.01.18 861
140 [QSMS-BK21 symplectic semiar] Part 4 (23' Aug 18 ~) qsms 2023.12.27 915
139 [QSMS Representation theory seminar 2023-12-28] Generalized polynomial functors qsms 2023.12.15 928
138 [QSMS Monthly Seminar 2023-12-14] Simple singularity and their friends qsms 2023.12.14 974
137 [QSMS Symplectic geometry seminar 2023-10-17, 18] New approaches to discovering symplectic non-convexity / Banach-Mazur distances in symplectic and contact geometry qsms 2023.10.10 977
136 [QSMS Monthly Seminar 2023-10-13] Quantum Grothendieck rings of Hernandez-Leclerc categories / Regular Schur labeled skew shape posets and their 0-Hecke modules qsms 2023.10.13 979
135 [QSMS Representation theory seminar - 2023-10-17] A Data-Scientific Approach to Representation Theory: Case Study of Kronecker Coefficients qsms 2023.09.27 998
134 [KMS Specical Conference with 2022 Fields Medalists] Related talks qsms 2023.10.11 1060
133 [QSMS Seminar 2023-12-13] A user’s guide to Schubert calculus of Lagrangian Grassmannians qsms 2023.11.27 1067
132 [QSMS Monthly Seminar 2023-11-11] Cluster structures on polygon spaces / From classical to quantum integrability qsms 2023.11.10 1076
131 [QSMS Monthly Seminar] Quiver Hecke algebras and open Richardson varieties qsms 2023.09.22 1079
130 [QSMS Symplectic geometry seminar 2023-10-24] Linear bounds on rho-invariants and simplicial complexity of manifolds qsms 2023.10.24 1099
129 [QSMS-BK21 Symplectic Seminar 9 June] Physical Aspects of the Calegaro System / Introduction to BV Formalism qsms 2023.06.26 1123
128 [QSMS Seminar 2023-05-17] Affinizations, R-matrices and reflection functors qsms 2023.05.04 1129
127 [QSMS-BK21 Symplectic Seminar 28 July] Nonexistence of Exact K(G,1) Lagrangians in Milnor Fibers of Weighted Homogeneous Polynomials / Associative Yang-Baxter Equation and Fukaya Categories qsms 2023.07.17 1137
126 [QSMS Monthly Seminar 2023-05-26] Lagrangian submanifolds and their Legendrian lifts qsms 2023.05.26 1138
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8