Mathematical Doctorants Seminar of the Luxembourg University
2015/2016

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General Information

Time and venue

The sessions take place every Thursday from 10:00 to 11:30, in the lecture room of the math library located in the math building (G) on the campus of Kirchberg.



Aim

Dedicated to Ph.D. students, the Doctorants Seminar is an important part of the research training offered at the Mathematics Research Unit of Luxembourg University. The Doctorants Seminar has a twofold objective:

• To give Ph.D. students the opportunity to present their fields of research and some topics and problems studied in those fields. The usual audience of the Doctorants Seminar is composed by Ph.D. students, young researchers and professors of the Mathematics Research Unit. The atmosphere is informal, so that all participants can ask the questions they want. Comments and suggestions on the presentations are also highly encouraged.
  
  
• To provide a good general mathematical background, in relation with the research interests of groups of Ph.D. students and other participants of the Doctorants Seminar. In this perspective, the Doctorants Seminar proposes all over the academic year series of introductory minicourses, held by the young researchers of the Mathematics Research Unit.

Who can be a speaker?

All contributions for talks or minicourses are welcome, including from people external to Luxembourg Mathematics Research Unit!
If you want to make a presentation, please provide the organizers with a title and an abstract of your talk. Lecture notes in any form are welcome as well.

Organisers

• Martin Olbrich
• Oleksandr Iena
• François Petit

Summer semester

• June 9, 2016 (This talk will take place in B 02)
  Hector Castejon-Diaz, "Hyperkähler Berezin-Toeplitz quantization and K3 surfaces"
  Abstract: K3 surfaces admit different quantum Hilbert spaces. By tensoring them, one can study a generalization of Berezin-Toeplitz operators in this new space. Such operators inherit the main properties of both the original Berezin-Toeplitz operators and the quaternionic numbers. My talk will be focused in introducing this new operators. I will review the main properties of quantization, but I will assume that everyone is familiar with the basic notions of K3 surfaces.
  

Summer semester: reading course "Singular points of complex hypersurfaces"

• January 28, 2016
  Organisational meeting of the seminar.
  Abstract: This semester the aim of the seminar will be to read some part of the book Singular Points of Complex Hypersurfaces by J. Milnor.
  
• February 4, 2016
  Hector Castejon-Diaz, "Elementary facts about complex algebraic sets I"
  
• February 11, 2016
  Assar Andersson, "Elementary facts about complex algebraic sets II"
  
• February 18, 2016
  Damjan Pistalo, "The curve selection Lemma"
  
• February 25, 2016
  Oleksandr Iena, "The Milnor's fibration theorem (I)"
  
• March 3, 2016
  Oleksandr Iena, "The Milnor's fibration theorem (II)"
  
• March 17, 2016
  Vladimir Salnikov, "Morse Theory I"
  
• March 24, 2016
  Olivier Elchinger, "Morse Theory II"
  
• April 7, 2016
  Florian Schatz, "The topology of the Milnor's fiber and of K I"
  
• April 14, 2016
  Stephen Kwok, "The topology of the Milnor's fiber and of K II"
  
• April 21, 2016
  Ronan Herry, "The Milnor's fiber of an isolated critical point"
  The slides of the talk are available here.
  
• April 28, 2016
  François Petit, "The middle Betti number of the Milnor's fiber"
  



Winter semester: reading course "K-theory"

The seminar had the form of a reading course on topological K-theory. The aim was to get a feeling for what K-theory is about. We mostly followed Atiyah's book K-theory. The detailed syllabus of the talks is available here.
• September 17, 2015
  François Petit & Sinan Yalin, Organisational meeting of the seminar.
  Abstract: This semester the seminar will mostly take the form of a reading course on topological K-theory. The aim is to get a feeling for what K-theory is about. We will mostly follows Atiyah's book K-theory.
  
• September 24, 2015
  François Petit, Elements of category theory.
  Abstract: In this talk we will review the elements of category theory used in Atiyah's book K-theory.
• October 1, 2015
  Alain Leytem, "Basics of vector bundles"
  
• October 8, 2015
  Olivier Elchinger, "Vector bundles on compact spaces"
  
• October 15, 2015
  Andrea Tamburelli, "Projective geometry for K-theory"
  
• October 29, 2015
  Damjan Pistalo, "Construction of the Grothedieck group and first properties"
  
• November 5, 2015
  Francois Petit, "Cohomological aspects of K-theory"
  
• November 12, 2015
  Gennaro di Brinno, "The long exact sequence for K-theory"
  
• November 19, 2015
  Stephen Kwok, "Atiyah-Bott periodicity and applications"
  
• November 26, 2015
  Florian Schatz, "Computations in K-theory"
  
• December 3, 2015
  Cancelled, "Finer structure of K-theory"
  
• December 10, 2015
  Sinan Yalin/Cancelled, "The Thom isomorphism"