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
Summer semester

June 9, 2016 (This talk will take place in B 02)
Hector CastejonDiaz, "Hyperkähler BerezinToeplitz quantization and K3 surfaces"
Abstract: K3 surfaces admit different quantum Hilbert spaces.
By tensoring them, one can study a generalization of BerezinToeplitz operators in this new space.
Such operators inherit the main properties of both the original BerezinToeplitz 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 CastejonDiaz, "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 "Ktheory"
The seminar had the form of a reading course on topological Ktheory. The aim was to get a feeling for what Ktheory is about. We mostly followed Atiyah's book Ktheory.
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 Ktheory. The aim is to get a feeling for what Ktheory is about. We will mostly follows Atiyah's book Ktheory.

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 Ktheory.

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 Ktheory"

October 29, 2015
Damjan Pistalo, "Construction of the Grothedieck group and first properties"

November 5, 2015
Francois Petit, "Cohomological aspects of Ktheory"

November 12, 2015
Gennaro di Brinno, "The long exact sequence for Ktheory"

November 19, 2015
Stephen Kwok, "AtiyahBott periodicity and applications"

November 26, 2015
Florian Schatz, "Computations in Ktheory"

December 3, 2015
Cancelled, "Finer structure of Ktheory"

December 10, 2015
Sinan Yalin/Cancelled, "The Thom isomorphism"