Jarníkovská přednáška prof. Teichnera

Peter Teichner se narodil v Bratislavě, po Pražském jaru v roce 1968 emigroval s rodinou do Německa. Doktorát obdržel v Mohuči v roce 1992 a v následujících letech spolupracoval s Mikem Freedmanem. Po semestrech na MPIM, IHES a MSRI se Teichner přemístil na Kalifornskou univerzitu do San Diega. V roce 2004 se pak stal profesorem na Kalifornské univerzitě v Berkeley. Zaměřuje se na matematické přístupy ke kvantové teorii pole a zejména na vztahy ke kohomologii. Od roku 2009 působí jako ředitel Institutu Maxe Plancka pro matematiku v Bonnu.

Abstrakt přednášky:

After recalling the Atiyah-Segal-Witten formalism for topological field theories (TFTs), we will explain some recent computations of Freed-Hopkins in the case of positive invertible TFTs. Their tables magically agree with computations made in condensed matter physics of gapped systems, namely for symmetry protected topological phases. In both approaches, the input is the space-time dimension d, together with a symmetry group H, and the output is a finitely generated abelian group TP(d,H) of topological phases. It remains an open question why these groups can be computed in two completely diff erent ways. For fixed dimension d, there is a 10-fold way in which the groups H arise, and we will show how they are related to the 8+2 super division algebras (over the real and complex numbers). We will prove that invertible TFTs are classified by their partition function, an invariant of closed d-manifolds with structure group H. Finally, we will characterize such manifold invariants in terms of a 4-term cut-andpaste relation and connect these back to the Freed-Hopkins computations. The last part is current joint work with Matthias Kreck and Stephan Stolz.

– OPMK –