| Wednesday 3 July 2024 | |
| Events for day: Wednesday 12 June 2024 |
| 10:00 - 11:00 Lecture Perturbed Uniform Spanning Forests School MATHEMATICS In this talk, we introduce a natural negatively dependent percolation model, which we call ?perturbed uniform spanning forest.? This model is an interpolation between "Bernoulli bond percolation" and "uniform spanning forest", two fundamental probabilistic models. We discuss a few interesting problems and go over some of our progress in analyzing this model. This talk is based on an ongoing work with Kasra Alishahi. Venue: Niavaran, Lecture Hall 1 ... 14:00 - 15:00 Combinatorics and Computing Weekly Seminar Partitions into Pairs with Prescribed Differences School MATHEMATICS Consider the following two general questions: - For an Abelian group $A$ of order $2n$ and nonzero elements $d_1, ldots, d_n$ of $A$, is it always possible to partition $A$ into pairs such that the difference between the two elements of the $i$th pair is equal to $d_i$? - For an Abelian group $A$ of order $2n+1$ and nonzero elements $d_1, ldots, d_n$ of $A$, is it always possible to partition $Asetminus{0} $ into pairs such that the difference between the two elements of the $i$th pair is equal to $d_i$? ... 15:30 - 17:00 Geometry and Topology Weekly Seminar Regularity and Persistence in non-Weinstein Liouville Geometry via Gyperbolic Dynamics School MATHEMATICS It is well known that the study of Liouville geometry, in the case of gradient-like Liouville dynamics, can be reduced to a Morse theoretical description in terms of symplectic handle decompositions. Such examples are called Weinstein. On the other hand, the construction and properties of non-Weinstein Liouville structures are far less understood. The first examples of non-Weinstein Liouville manifolds were constructed by McDuff (1991) and Geiges (1995), which were later on generalized by Mitsumatsu (1995), hinting towards further interactions with hyperbolic dynamics. More specifically, Mitsumatsu proved that given an arbitrary closed 3-mani ... 17:30 - 19:00 Algebraic Geometry Biweekly Webinar Hilbert Functions, Lefschetz Properties and Perazzo Hypersurfaces School MATHEMATICS Artinian Gorenstein algebras (AG algebras for short) can be viewed as algebraic analogues of the cohomology rings of smooth projective varieties. The Strong and Weak Lefschetz properties for graded AG algebras take origin from the hard Lefschetz theorem. The properties of an AG quotient $A _F$ of a polynomial ring are related to its Macaulay dual generator $F$, and in particular $A_F$ fails the Strong Lefschetz property if and only if the hessian of $F$ of order $t$ vanishes for some $1leq tleq d/2$, where $d=deg F$ and the usual hessian is obtained for $t=1$. Perazzo polynomials are a large class of polynomials with vanishing hessian so ... |