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


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)
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
16.12.2021Michał Jesionowski
13.01.2022Paweł Poczobut
20.01.2022Piotr Oszer
27.01.2022meeting cancelled
Spring term
03.03.2022Mieszko Zimny
10.03.2022Katarzyna Krawiec
17.03.2022Mateusz Kobak
24.03.2022Jarosław Ławnicki(Log-)minimal model programme
31.03.2022Michał Szachniewicz Globally Valued Fields - connections to Yau's theorem, Nevanlinna theory, and Arakelov geometry.
07.04.2022Mateusz LowielOrderable groups (advisor: Wojciech Politarczyk)
21.04.2022Michał ŁupińskiFoliations
28.04.2022Piotr OszerCyclic quotient singularities and their resolutions on surfaces
05.05.2022Mieszko ZimnyAlbanesse on surfaces
12.05.2022Paweł Poczobut
19.05.2022Michał Jesionowski
26.05.2022Patryk Szlufik
02.06.2022Katarzyna Krawiec
09.06.2022Mateusz Kobaklast 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 - Cantat Déserti Xie Three chapters on Cremona groups In addition: - Cantat Lamy Normal subgroups in the Cremona group - Dolgatchev Finite subgroups of the plane Cremona group - Blanc Relations in the Cremona group over perfect fields
  3. Spherical varieties. Brion has good and brief introductions to this topic: (about actions of algebraic groups on manifolds/varieties) (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.