Time: 16:30-18:00

Location: Mondi 3 / Central Building

Speaker 1: Paul Hametner (first year student)

Title: The Minimum Degree Question for the Maker-Breaker Domination Game

Abstract: Let G be a finite simple graph, and consider the Maker-Breaker Domination game on G. The rules of this game are the following: two players, Dominator and Staller, alternately claim one not yet claimed vertex of G until all the vertices are claimed and the game ends. At the end of the game, Dominator wins if his vertices form a dominating set of G. Otherwise, Staller wins. Given a non-negative integer d, the minimum degree question asks for the smallest integer n(d) such that there exists a graph G on n(d) vertices and of minimum degree d such that Staller has a winning strategy on G going second. In this talk we prove upper and lower bounds for n(d) and outline how to compute n(3).

Joint work with Jakob Führer, Georg Grasegger, and Oliver Roche-Newton.

Speaker 2:  Michiel de Wilde (first year student)

Title: Classification of locality preserving symmetries on spin chains

Abstract: We consider the action of a finite group G by locality preserving automorphisms (quantum cellular automata) on quantum spin chains.  We refer to such group actions as "symmetries". The natural notion of equivalence for such symmetries is stable equivalence, which allows for stacking with factorized group actions. Stacking also endows the set of equivalence classes with a group structure. We prove that the anomaly of such symmetries provides an isomorphism between the group of stable equivalence classes of symmetries with the cohomology group H^3(G,U(1)), consistent with previous conjectures. This amounts to a complete classification of locality preserving symmetries on spin chains. We further show that a locality preserving symmetry is stably equivalent to one that can be presented by finite depth quantum circuits with covariant gates if and only if the slant product of its anomaly is trivial in H^2(G, U(1)[G]).