Delphine Pol
Address : Department of Mathematics
Hokkaido University
Kita 10, Nishi 8, Kita-ku
Sapporo 060-0810, Japan
e-mail:
pol
[_at_]
math.sci.hokudai.ac.jp
Office : 4-515
(Campus map)
French version
Doctor in Mathematics, I am now a Postdoctoral fellow at the University of Hokkaido under the supervision of Professor Masahiko Yoshinaga with a postdoctoral fellowship of the Japan Society for the Promotion of Science (JSPS) (Postdoctoral Fellowship (Short-term) for North American and European Researchers). From October 2018, I will be a postdoctoral fellow at T.U. Kaiserslautern under the supervision of Prof. Dr. Mathias Schulze, with a Humboldt postdoctoral fellowship.
Research interest: Algebraic geometry, free singularities, curve singularities, subspace arrangements, logarithmic forms and vector fields, logarithmic residues, semigroup and set of values of ideal along curves
Member of the GDR Singularités et Applications, GDR CNRS 2945
Thesis
I defended my PhD thesis whose title is Free singularities, logarithmic forms and residues on December, 8th 2016 at the University of Angers (France). The jury was:
Abstract: We study in this PhD thesis the logarithmic differential forms along a reduced singular equidimensional space of any codimension embedded in a smooth manifold. We develop a notion of free singularities which extend the notion of Saito free divisor. Our first purpose is to give characterizations of freeness for Cohen-Macaulay spaces which generalize the hypersurface case. We then consider the case of curves, for which we generalize Delgado's theorem of the symmetry of the semigroup to any fractional ideal and its dual. We use this result to study the module of logarithmic residues, in particular in an equisingular deformation of a plane curve. We also compute explicitely a free resolution of the module of logarithmic forms of a reduced quasi-homogeneous complete intersection curve.
Research documents
Publications
- On the values of logarithmic residues along curves, Annales de l'Institut Fourier, 68 no. 2 (2018), p. 725-766, doi: 10.5802/aif.3176
- Logarithmic residues along plane curves, C. R. Math. Acad. Sci. Paris 353 (2015), no. 4,
345–349., 2015, doi : 10.1016/j.crma.2015.02.002
Preprints
- On a generalization of Solomon-Terao formula for subspace arrangements, arXiv:1803.08672, submitted
- Symmetry of maximals for fractional ideals of curves, arXiv:1802.07901, submitted
- Characterizations of freeness for Cohen-Macaulay spaces, arXiv:1512.06778, submitted
Thesis
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Awards and fellowships
- Humboldt Research Fellowship for Postdoctoral Researcher, 2 years from October 2018, Kaiserslautern (Germany) under the supervision of Mathias Schulze
- Postdoctoral fellowship from the Japan Society for the Promotion of Science (JSPS) Short-term (one year),
- Third price for the poster Plane curves and the symmetry of values, JDoc 2015, April, 9th 2015, Angers, France
- Doctoral fellowship from Angers Loire Métropole.
Talks and posters
Conference talks
- Matroids, reflection groups, and free hyperplane arrangements, June, 11th-15th 2018, RIMS Kyoto, Japan
- Branched Coverings, Degenerations, and Related Topics 2018, March, 5th-9th 2018, Hiroshima, Japan
- A walk between hyperplane arrangements, computer algebra and algorithms, January 31th-February 2nd 2018, Sapporo, Japan
- The 4th Franco-Japanese-Vietnamese Symposium of Singularities, November, 7th-11th 2016, Chambéry, France
- Atelier Jeunes Chercheurs en Singularités, April, 25th-30th 2016, Nice, France
- Rencontres doctorales Lebesgue 2015 28th-30th 2015, Nantes, Franceslides
- Geometry, Topology and Combinatorics of Hyperplane Arrangements and Related Problems, September, 14th-18th 2015, Zaragoza, Spain slides
Seminar talks
- Shinshu Topology seminar, September, 3rd 2018, Matsumoto, Japan
- TMU Seminar on complex geometry, July 11th, 2018, Tokyo, Japan
- Séminaires systèmes dynamiques et géométrie, May 22th 2018, Angers, France
- Discrete Geometric Structure Seminar, March 29th 2018, Sapporo, Japan
- Workshop "Problems around hyperplane arrangements", March 15th 2018, Sapporo, Japan
- Workshop on algebraic surfaces at Akihabara, 27th January 2018, Tokyo, Japan
- Discrete Geometric Structure Seminar, October 19th and October 26th 2017, Sapporo, Japan
- Séminaire Géométrie et Système dynamiques, Dijon, France, March, 23th 2017
- Séminaire Système dynamiques, Toulouse, France, March, 17 2017
- Séminaire sur les singularité, Paris, France, February 28th 2017
- Séminaire Quimpériodique, Quimper, France, January, 19th-20th 2017
- Séminaire de Géométrie Algébrique Laboratoire Angevin de REcherche en Mathématiques, Angers, France, November, 4th 2016
- Séminaire de Géométrie Complexe, Institut Elie Cartan de Lorraine, Nancy, France, May, 23th 2016
- Séminaire de Géométrie, Institut Mathématiques de Bordeaux, Bordeaux, France, January, 15th 2016
- Groupe de travail "Symétrie miroir en termes de variétés de Frobenius" Laboratoire Angevin de REcherche en Mathématiques, Angers, France, December, 17th 2015
- Séminaire de Géoétrie des espaces singuliers, Laboratoire Paul Painlevé, Lille, France, October, 20th 2015
- Séminaire de Singularités, Technische Universität Kaiserslautern, Kaiserslautern, Allemagne, October, 8th 2015
- Séminaire de Géométrie Algébrique, Laboratoire Angevin de REcherche en Mathématiques, Angers, France, October, 10th 2014
Talks in PhD students workshop in geometry
- April 2016: An introduction to D-modules
- August 2014: Commutative algebra
- August 2013: Sheaf Cohomology
Poster
- The 5th Franco-Japanese-Vietnamese Symposium on Singularities, October 29th-November 3rd 2017, Kagoshima, Japan
- Free singularities and logarithmic residues, A panorama on Singular Varieties in honor of Le Dung Trang, February 7th-10th, Sevilla, Spain
- Plane curves and the symmetry of values, JDoc 2015, April, 9th 2015, Angers, France
- Logarithmic residues along plane curves, Doctoral course Introduction to Artin Approximation and the geometry of power series spaces, January 26th-30th 2015, CIRM, Marseille, France
Research stays
- Kaiserslautern (Germany), 05/10/2015-09/10/2015
- Tokyo (Japan), 09/07/2018-15/07/2018
- Fukuoka (Japan), 29/08/2018-01/09/2018
- Matsumoto (Japan), 03/09/2018-05/09/2018
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Meeting organization
Teaching
2016-2017
- Frist year undergraduate L1 MPCIE (Mathematics, Physics, Chemistry, Informatics, Economics):
- Course of Mathematics Upgrading
- Course of Calculus: complex numbers, functions
- Course of elementary linear algebra: vector spaces, matrices
- "Colles": oral exams for calculus and linear algebra
- Second year undergraduate L2 MPCIE:
- Teaching assistant for bilinear algebra: quadratic forms, lectures by Laurent Evain
2015-2016 and 2014-2015
- Frist year undergraduate L1 MPCIE:
- Course of Mathematics Upgrading
- Second year undergraduate L2 MPCIE:
- Teaching assistant for analysis: functions sequences and series, lectures by Laurent Meersseman
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