Gabriel Fazoli (Rennes)
Abstract:
A pencil of plane curves determines a foliation on the projective plane which, generically, has exactly $d^2$ radial singularities, and apart from these singularities, the foliation is locally given by closed holomorphic 1-forms. In this talk, we will prove the converse statement: a foliation of degree $2d-2$ on the projective plane with singularities of this type, under generic conditions, is determined by a pencil of curves. In other words, every degree $d$ curve passing by the radial singularities is invariant. In order to do that, we will introduce the notion of flat partial connections and relate the existence of flat meromorphic extensions of a flat partial connections with the existence of invariant curves.
10:30 • Universität Basel, Seminarraum 00.003, Spiegelgasse 1
Eva Miranda (Universitat Politècnica de Catalunya)
Singular Symplectic Manifolds
13:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Igor Shparlinksi (UNSW Sidney)
Artin\'s conjecture on average and short character sums abstract
Abstract:
Let N_a(x) denote the number of primes up to x for which the integer a is a primitive root. We showthat N_a(x) satisfies the asymptotic predicted by Artin\'s conjecture for almost all1\\le a\\le exp((log log x)^2). This improves on a result of Stephens (1969) which applies to themuch longer range 1 \\le a \\le exp(6(log x log log x)^{1/2} )). A key ingredient in the proof is a new shortcharacter sum estimate over the integers, improving on the range of a result of Garaev (2006).Joint work with Oleksiy Klurman and Joni Teräväinen.
14:15 • EPF Lausanne
Lorenzo La Porta (University of Padova)
Singularities in the Ekedahl--Oort stratification abstract
Abstract:
I will discuss recent results on the singularities of unionsof Ekedahl--Oort strata in the special fibres of some Shimura varieties.These results were obtained by studying the geometry of some natural period spaces in positive characteristic, the stacks of G-zips, and their relative flag spaces. I will present the main theorems, mention some applications and provide an overview of the techniques involved.This is joint work with Jean-Stefan Koskivirta and Stefan Reppen.
Pavel Mnev (Notre Dame)
Globalization of Chern-Simons theory on the moduli space of flat connectionsd abstract
Abstract:
Path integral of Chern-Simons theory on a closed 3-manifold gives a family of perturbative partition functions (effective BV actions induced on twisted de Rham cohomology) parametrized by the moduli space of flat connections. This family is horizontal with respect to the Grothendieck connection modulo a BV-exact term. I will outline how (a) this family can be extended to a nonhomogeneous form over triples (kinetic flat connection, gauge-fixing flat connection, metric), satisfying a differential quantum master equation (i.e., is annihilated by an appropriate “Gauss-Manin” flat superconnection);(b) one extract from the extended partition function above a volume form on the smooth irreducible stratum of moduli space, whose cohomology class is metric-independent, and hence yields an invariant of a framed 3-manifold.The talk is based on a joint work with Konstantin Wernli, arXiv:2510.18653 [math-ph]
15:00 • Université de Genève, Conseil Général 7-9, Room 1-07
Dr. Antoine Detaille (ETH Zürich, Switzerland)
About some approximation problems for Sobolev maps to manifolds abstract
Abstract:
In a striking contrast with the classical case of real-valued Sobolev functions, a Sobolev map with values into a given compact manifold N need not be approximable with smooth N-valued maps. This observation, initially due to Schoen and Uhlenbeck (1983), gave rise to a whole area of research concerned with questions related to approximability properties of Sobolev mappings with values into a compact manifold. In this talk, I will give a broad overview of this research direction, its history, the main problems it is concerned with, important known results, as well as some recent contributions.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Jonathan Pim (University of Helsinki)
Nodal resolution of quasiregular curves via bubble trees abstract
Abstract:
I will discuss normal and quasinormal families of quasiregular curves, and in particular how studying the latter leads to a version of Gromov\' compactness theorem for quasiregular curves into manifolds of bounded geometry via bubbling of the domain. This bubbling process transforms the domain into a bubble tree over the original manifold and our procedure for extending quasiregular curves over bubbles requires us to pass to a more general class of mappings which are only asymptotically quasiregular. However, after the inductive bubbling process terminates, the sequence which has been extended to the bubble tree, converges locally uniformly to a true quasiregular curve on the bubble tree. On one hand, this limiting curve may be interpreted as a weak and non-unique replacement for the classical locally uniform limit of the original sequence. On the other hand, the measure it induces may be seen as a resolution of the singular parts of the limiting measure of the original sequence. As a corollary we obtain a normality criterion for families of quasiregular curves.Quasiregular curves are a class of mappings between non-equidimensional oriented Riemannian manifolds which includes both the classical quasiregular mappings and Gromov\'s pseudoholomorphic curves. They are defined with respect to a calibration i.e. a smooth closed form with unit comass. This calibration is used to define a replacement for the distortion inequality and the mapping induces a measure on its domain via the pullback of this calibration. The calibration gives, in some sense, the allowed directions for the curve, while the distortion constant controls both the curve\'s deviation from these allowed directions and the classical distortion.
15:15 • Université de Fribourg, PER23 room 0.05
Francesco Lin (Columbia University)
Geometry and topology of vector fields in three-dimensions abstract
Abstract:
Understanding the locus at which a vector field on a manifold vanishes (or, more generally, k-vector fields are linearly dependent) is a fundamental problem in geometry and topology, dating back at least to the famous Hairy Ball theorem. In this talk, I will discuss some of the history of the problem, with a focus on three dimensions, and discuss a new proof using the Dirac equation of the following theorem of Gromov (and in fact a Riemannian refinement of it): on a closed three-manifold equipped with a volume form, there exist three-vector fields which are volume-preserving and are linearly independent at every point.
16:00 • Université de Neuchâtel, Rue Emile-Argand 11, Room B013
Yasaman Asgari (Universität Zürich)
What is... temporal network? abstract
Abstract:
<p><span style="color: black; font-size: 12pt; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif;" data-olk-copy-source="MessageBody">Temporal networks offer a unique lens on complex systems that constantly change, where connections form, dissolve, and reappear, much like friendships in our own lives. While static networks capture a single moment, like a photograph, temporal networks reveal how structures evolve over time, shaping the dynamics that unfold on them. This perspective is crucial for questions ranging from disease spread to predicting where a PhD student may end up after graduation. In my talk, I begin with homophily, how similarities influence our social interactions, and show how random walks provide a richer, more dynamic understanding of these patterns. I then extend this to temporal networks and introduce a method for quantifying homophily across time scales, addressing a long-standing gap in the field. Throughout, I highlight the iterative nature of complex systems research: refining questions, adapting mathematical tools, scaling analyses with distributed computing, and grounding insights in empirical data, because every dataset tells its own story.</span></p>
16:30 • UZH Zentrum, Building KO2, Room F 150
Prof. Dr. Yilin Wang
Geometry of Surfaces through the lens of Probability
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG , Room F 30