Topology and geometry of manifolds (TiGR)

Master seminar 2020/2021

This is out of date description of an old seminar.
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Organisers: Jarosław Buczyński and Krzysztof Ziemiański

Time of meetings

Thursdays, 8:30-10:00

Place of meetings



15.10.2020 J.B. i K.Z.

Jarosław Ławnicki,

Michał Łupiński,
Kristian Olechowski
Organisation, presentation of the subject and planning of schedule,
then presentations on Master theses in preparation:

Embeddings of curves into surfaces and the complement problem (advisors: Karol Palka, Jarosław Wiśniewski)
Singularities of foliations on algebraic surfaces (advisor: Adrian Langer)
Derived categories and perverse sheaves (advisor: Agnieszka Bodzenta)
Mykola Shameiev,
Kamil Szubiński,
Katarzyna Krawiec,
Mateusz Zugaj,
Michał Szachniewicz,
Piotr Rudnicki
Presentations on Master and BSc theses or other projects:
Semiorthogonal decompositions of derived category of coherent sheaves (advisor: Agnieszka Bodzenta)
Graph Classes with fmNIP property (advisor: Szymon Toruńczyk)
Heegaard's diagrams (advisor: Andrzej Czarnecki)
Applications of ultracategories in logic (advisor: Marek Zawadowski)
Białynicki-Birula decomposition for $\mathbb{G}_m$ actions on affine schemes (advisor: Joachim Jelisiejew)
First glimpse on equivariant cohomology theory
29.10.2020Oskar Słowik,
Mateusz Kobak
Cohomological invariants of space of quatnum states (advisor: Andrzej Weber)
Book by Brendon: Section I.1, G-complexes; notes from the talk.
5.11.2020Paweł Poczobut,
Krystian Olechowski
An algebraic variant of Fischer-Grauert's Theorem (advisors: Piotr Achinger, Adrian Langer)

Section I.2, Equivariant cohomology theories; notes from the talk.
12.11.2020no meetingOn this Thursday the whole department has Wednesday classes
19.11.2020 Piotr Oszer
Majid Bigdeli
Berezinian from cohomological point of view (advisor: Andrzej Weber)
Equivariant cohomology: definition, coefficient systems
26.11.2020 Kunal Dutta,
Mateusz Zugaj
Proposal of MSc project on "Randomization in Computational Geometry and Topology"
Examples of equivariant cohomologies
03.12.2020 Mateusz Kobak,

Chirantan Mukherjee
Category of finite covering spaces of a connected topologigal space as an example of Galois category (advisor: Andrzej Weber)
10.12.2020 Karol Janowicz,
Paweł Poczobut
Units in rings of algebraic integers (advisor: Zbigniew Marciniak)
Spectral sequence(s)
17.12.2020Magdalena Karaś,
Katarzyna Krawiec
Property A in coarse geometry (advisor: Andrzej Nagórko)
Equivariant obstruction theory
07.01.2021Majid Bigdeli,
Jarosław Ławnicki
The Cyclic Homology of the Group Algebras (advisor: Massoud Amini)
Primary obstructions
14.01.2021Makar Veramchuk,
Michał Łupiński
Weighted $L_p$ inequalities for maximal function (advisor: Veniamin Krotov)
The characteristic class of a map; notes from the talk.
21.01.2021Chirantan Mukherjee
Piotr Rudnicki
Weakly globular double categories and weak units (based on arXiv:2008.11180 by Simona Paoli)
Hopf $G$-spaces and Eilenberg-MacLane $G$-complexes
28.01.2021Jeremi Zglinicki
Oskar Słowik
Constant curvature metrics on closed surfaces (advisor: Stefan Jackowski)
Function spaces and $G$-spectra
Spring term
04.03.2021Michał Szachniewiczwe commence the book by Atiyah on K-theory
11.03.2021Piotr OszerConstructions and basic properties of vector bundles
18.03.2021Kamil SzubińskiG vector bundles
25.03.2021Magdalena KaraśCell structures on Grassmannians
8.04.2021Karol JanowiczBasic definitions of K-theory
15.04.2021Mykola ShamaievThe Fundamental Product Theorem
22.04.2021Jeremi ZgnilickiK-theory as a cohomological theory and Bott periodicity
29.04.2021Dorota Jankowska(Short lecture) Type of equivariant Khovanov homotopy for some toric knots
(Longer lecture) K-theory follow up
6.05.2021Organisational meeting
13.05.2021Makar Veramchuk
20.05.2021Jarosław ŁawnickiThe Adams operations
27.05.2021Kristian OlechowskiStiefel-Whitney and Chern classes
10.06.2021Michał ŁupińskiEuler and Pontryagin classes

We are studying:

Further topic suggestions



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.