* Dates within the next 7 days are marked by a star.
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
* Monday 15 June 2026, 09:00, M237
Further information
Ohjelma: https://mycourses.aalto.fi/course/view.php?id=34597#module-908887
Anthony Mäkelä (University of Gothenburg)
Moduli of $P$-critical connections via moment maps and analytic GIT
* Monday 15 June 2026, 14:15, M3 (M234)
The Kobayashi--Hitchin correspondence relates stable holomorphic vector bundles to special connections, and can be viewed as a prototype for a broader principle: extremal objects in differential geometry should correspond to stable objects in algebraic geometry. Motivated by Bridgeland stability conditions, recent work has introduced polynomial curvature equations for Hermitian vector bundles, including (Z)-critical and (P)-critical connections, which generalize the Hermite--Einstein equation and admit moment-map interpretations. In this talk, I will describe a construction of moduli spaces for (P)-critical connections using local deformation theory and analytic geometric invariant theory. The construction produces finite-dimensional analytic GIT quotient charts around a (P)-critical connection and glues them into a Hausdorff complex space carrying a natural Weil--Petersson-type geometry.
AGC Seminar
Hermanni Huhtamäki (Aalto)
Maisterintutkielmaesitelmä: Jonesin polynomin kategoriointi ja topologinen kvanttikenttäteoria
* Wednesday 17 June 2026, 14:15, M3 (M234)
Jonesin polynomi on yksi tunnetuimmista solmutunnuksista. Esityksen tavoitteena on yleistää se Hovanovin homologiaksi. Ensimmäisessä vaiheessa Kauffmanin sulkeet esitetään oioskuutiona: sen kärjet ovat yksiulotteisia monistoja, jotka vastaavat oiottuja solmukaavioita, ja särmät ovat niiden välisiä kaksiulotteisia pienoja. Toisessa vaiheessa oioskuutio kuvataan topologisella kvanttikenttäteorialla porrastetuiksi vektoriavaruuksiksi ja niiden välisiksi kuvauksiksi, jotka muodostavat Frobeniuksen algebran. Näin saadaan ketjukompleksi, josta määritetään Hovanovin homologia Jonesin polynomia vahvempi solmutunnus. Lopuksi käydään yleisesti läpi topologisen kvanttikenttäteorian ominaisuuksia.
The talk will be in Finnish, below is a short English translation of the abstract:
We categorize the Jones polynomial by applying a (1+1)-dimensional topological quantum field theory (TQFT) to the cube of resolutions of a knot diagram. This TQFT is a symmetric monoidal functor that maps 1-dimensional manifolds to graded vector spaces and (1+1)-dimensional cobordisms to linear maps, equipping these vector spaces with the structure of a Frobenius algebra. In this way, we obtain Khovanov homology.
AGC Seminar
BSc Jussi Häkkänen (Aalto University)
TBA (MSc presentation)
Monday 22 June 2026, 13:15, M2 (M233)
Aalto Stochastics & Statistics Seminar
Gerald Williams (University of Essex)
TBA
Tuesday 23 June 2026, 14:15, M3 (M234)
AGC Seminar
Jules Martel (Cergy Paris University)
Towards a homological reconstruction of TQFTs
Tuesday 30 June 2026, 10:15, M3 (M234)
TQFTs are this idea of Witten that we can study quantum field theories from the point of view of the topology of state spaces and of topological transitions. Mathematically, it was formalised by Atiyah as a linearization of a cobordism category. It was concretely realized by ReshetikhinTuraev (RT) coupled with BlanchetHabbegerMasbaumVogel universal construction. The RT philosophy relies on a diagrammatic model for cobordisms (based on knot diagrams) and uses modules on quantum groups (or more generally monoidal categories) to linearly model these diagrams. This has more recently been extended so to permit the utilization of non semisimple monoidal categories as input of the construction giving rise to a new generation of TQFTs, for which a nice example is the KerlerLyubashenko (KL) construction. These constructions need abstract algebra tools applied on diagrammatic representations of manifolds, and we will try to avoid this by using homology theories, allowing a more global definition of TQFTs.
In this talk I'll introduce a new philosophy to build TQFTs based on homology of configuration spaces. Representations of mapping class groups constitute an important byproduct of TQFTs, while more natural ones can be built out of twisted homologies of configuration spaces of surfaces. We will show that from this latter new framework we can recover step by step the properties of KL TQFTs associated with quantum groups and even a unifying framework. Ill stay introductory most of the talk but the constructions and their motivations will be the occasion to review joint works with: S. Bigelow, M. De Renzi, R. Detcherry or Q. Faes (depending on the time).
Mathematical physics seminar
Prof. Timothy Trudgian (UNSW Canberra)
Division!
Thursday 09 July 2026, 15:15, M3 (M234)
Euclids algorithm for division allows us to divide two numbers, keep track of remainders, and recover GCDs. I will discuss other algebraic settings: some rings are known to be Euclidean (meaning they have this algorithm), some are known not to be; many are unknown. I will end with a summary of recent work done in this article that resolves completely the case of cyclic cubic fields:
https://arxiv.org/abs/2507.05862
ANTA Seminar / Hollanti et al.
Prof. Guillermo Mantilla-Soler (U. Nacional de Colombia)
TBA
Tuesday 25 August 2026, 15:15, M3 (M234)
ANTA Seminar / Hollanti et al.
Lorenzo Zacchini (Aalto University)
TBA (midterm review)
Wednesday 23 September 2026, 10:15, M3 (M234)
Analysis seminar / Hytönen
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