Jorge Fariña Asategui (Université de Genève)
Maximal subgroups of infinite index in branch groups abstract
Abstract:
A finitely generated infinite group may or may not admit maximal subgroups of infinite index. For certain families of groups, such as linear groups, it is completely characterised when they admit maximal subgroups of infinite index. For the class of branch groups, it was Bondarenko who constructed the first example admitting maximal subgroups of infinite index. These groups are very special, as they contain copies of themselves. Apart from these groups, which always act on regular rooted trees of degree at least 5, there is only one example of a branch group with maximal subgroups of infinite index, which acts on the binary rooted tree. In particular, there is no example acting on a regular rooted tree of degree 3 or 4.In this talk, we introduce a new construction which produces an infinite family of branch groups with maximal subgroups of infinite index and acting on regular rooted trees of any degree. This is joint work with Anitha Thillaisundaram.
13:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Ana Pavlaković
χ-Independence for BPS Invariants of Some Local Surfaces abstract
Abstract:
Curve counting on Calabi--Yau threefolds admits several seemingly different formulations. Gromov--Witten theory gives rational virtual counts of stable maps, while the Gopakumar--Vafa conjecture predicts that these should be expressible through integral invariants. Maulik--Toda proposed a sheaf-theoretic definition of these invariants using moduli spaces of sheaves with fixed Euler characteristic $\\chi$. Since the corresponding Gromov--Witten theory involves no such choice of $\\chi$, these invariants can represent the BPS invariants predicted by Gopakumar--Vafa only if they are, a posteriori, independent of $\\chi$. This is Toda’s $\\chi$-independence conjecture, and its verification provides evidence for the expected GW/GV correspondence.I will explain $\\chi$-independence for a class of local surfaces that can be viewed as twisted analogues of local curves, using dimensional reduction to relate the problem to the Hitchin fibration, where $\\chi$-independence is known.
13:15 • EPF Lausanne, CM 1 517
Shihao Zhu (Ulm University)
Nonconcave Portfolio Choice under Smooth Ambiguity abstract
Abstract:
How should an investor allocate assets when the expected return itself is uncertain and the payoff from investment is nonlinear? These features arise naturally in delegated portfolio management and are also relevant to insurance products with guarantees and embedded options. We study this question in continuous time using smooth ambiguity, which distinguishes investment risk from uncertainty about which expected-return model to trust, while allowing beliefs to be updated from market prices. Using a robust representation and a minimax argument, we decompose the initial smooth-ambiguity evaluation into a family of Bayesian portfolio problems under ambiguity-adjusted beliefs. Each fixed-belief problem is time-consistent and can be solved using nonlinear filtering and martingale methods, yielding explicit fixed-prior trading rules. In an application to convex incentive contracts, nonlinear payoffs generate an all-or-nothing pattern in terminal wealth and can encourage aggressive risk-taking. Our numerical analysis illustrates that greater ambiguity aversion shifts weight toward adverse return scenarios, narrows the range of states in which aggressive positions are attractive, and lowers risky-asset exposure.Seminar organized by Prof. Havrylenko
14:00 • EPF Lausanne, Extranef 110
Alan Reid (Rice University)
Arithmetic groups and their profinite completions
14:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Daniel Galvin (UT Austin)
Non-smoothable surfaces in the 4-sphere