Topology and geometry of manifolds (TiGR)

Master seminar 2021/2022

Organisers: Jarosław Buczyński and Krzysztof Ziemiański

Time of meetings

Thursdays, 8:30-10:00

Place of meetings

MIMUW, room 3240


Schedule:

When?Who?What?
7.10.2021 J.B. i K.Z.

Paweł Poczobut,

Mateusz Kobak

Organisation, presentation of the subject and planning of schedule,
then presentations on Master theses in preparation:
Twierdzenie Grauerta-Fischera w dodatniej charakterystyce (Grauert-Fischer Theorem in positive characteristic)
Oswojona grupa podstawowa dla analitycznych przestrzeni adycznych (Tame fundamental group for adic analytic spaces)
14.10.2021
Piotr Oszer,
Katarzyna Krawiec,

Michał Jesionowski,
Mieszko Zimny
Kuba Krawczyk
Presentations on Master and BSc theses or other projects
Linie na rozmaitościach rzutowych (lines on projective varieties)
Rozkład Heegarda, homologie Heegarda-Floera, trysekcje czterowymiarowych rozmaitości (Heegard decomposition, Heegard-Floer homology, and trisections of four dimensional manifolds)
Geometryczna teoria grup i Z-struktury (Geometric grup theory and Z-structures)
Kongruencje dla szeregów Laurent (Congruences for Laurent series)
Struktura algebroidu Atiyah (Sturcture of Atiyah's algebroid)
21.10.2021Kuba KrawczykResolution of singularities: Newton's method
28.10.2021Michał Jesionowski
04.11.2021Mieszko Zimny
18.11.2021Paweł Poczobut
25.11.2021Piotr Oszer
02.12.2021Mateusz Kobak
09.12.2021Katarzyna Krawiec
16.12.2021Piotr Giczewski
13.01.2022
20.01.2022
27.01.2022
Spring term
03.03.2022
10.03.2022
17.03.2022
24.03.2022
31.03.2022
07.04.2022
21.04.2022
28.04.2022
05.05.2022
12.05.2022
19.05.2022
26.05.2022
02.06.2022
09.06.2022last meeting

We are studying:


Further topic suggestions

  1. Coxeter groups, following the books: Hiller, Howard - Geometry of Coxeter groups, Huphreys, Coxeter groups. This is related to homogeneous spaces and group actions on manifolds. I find this topic very useful, although a little boring and tedious (very algebraic).
  2. Cremona Groups – another classic topic, we can study the plane case, or algebraic properties of the group or its geometric properties or its dynamical properties. - Cantat – The Cremona group https://claymath.org/sites/default/files/canat.pdf - Cantat Déserti Xie Three chapters on Cremona groups https://arxiv.org/abs/2007.13841 In addition: - Cantat Lamy Normal subgroups in the Cremona group https://arxiv.org/abs/1007.0895 - Dolgatchev Finite subgroups of the plane Cremona group https://arxiv.org/abs/math/0610595 - Blanc Relations in the Cremona group over perfect fields https://arxiv.org/abs/1011.4432
  3. Spherical varieties. Brion has good and brief introductions to this topic: https://www-fourier.ujf-grenoble.fr/~mbrion/notes_luminy.pdf (about actions of algebraic groups on manifolds/varieties) https://link.springer.com/chapter/10.1007/978-1-4612-3702-0_3 (about spherical varieties) I would have to look up some further readings and the base book.
  4. another proposal would be to try real algebraic and semi-algebraic geometry. I think there is no course in this topic at our University, but it is fairly large and interesting topic I am not familiar with. I would have to discuss with some people from UJ (Kraków) what are the possible books and references.

  5. Announcements:

    Some NCN grants have a possibility of awarding a scholarships for writing MSc thesis. Grants that we know about and might have this possibility (and whose topics is related to the interests of the seminar) are:

    Please contact the Principal Investigator of the respective grant if you are interested.