* Dates within the next 7 days are marked by a star.
Joel Hakavuori (Sorbonne University, IMJ-PRG)
Unimodality, Lefschetz theory, and F-purity
* Today * Monday 31 August 2026, 14:15, M3 (M234)
The g-conjecture for simplicial spheres and the Hibi-Ohsugi conjecture for IDP reflexive lattice polytopes are unimodality conjectures for face-number data and lattice-point enumerators, respectively. In both cases, these sequences occur as the Hilbert function of an associated Artinian Gorenstein algebra, and the desired unimodality follows from a Lefschetz property for that algebra. Recent proofs in characteristic 2 replace the positivity arguments familiar from the classical theory of simplicial polytopes by an anisotropy argument: using a generic Artinian reduction, identities for the volume map, and differentiation identities, one proves that nonzero elements up to the middle degree have nonzero squares, which is eventually used to prove that a generic linear form is a Lefschetz element.
I will explain how these ideas are abstracted and generalized in recent work of Adiprasito, Katz, Oba, Papadakis, and Petrotou (2605.02479). They study how the volume and Frobenius maps interact for generic Artinian reductions of CohenMacaulay rings, and in the Gorenstein case produce a polynomial called the Parseval core. A combinatorial condition on its monomial support, called p-conducting, guarantees a nonvanishing result that implies anisotropy and Lefschetz in characteristic 2. I will then explain how Fedders criterion shows that the Parseval core of an F-pure Gorenstein ring is 2-conducting. This unifies the characteristic 2 proofs of the g- and Hibi-Ohsugi conjectures, while also yielding Lefschetz properties for many other classes of interesting Gorenstein rings in positive characteristic.
AGC Seminar
BSc Julia Virtanen (Aalto University)
How ordering policies shape the upstream demand signal: a distributional analysis (MSc presentation)
* Thursday 03 September 2026, 15:15, M3 (M234)
Understanding the demand signal is important for forecasting, but the upstream demand signal is generally known to be harder to forecast due to the bullwhip effect. Consumer demand is transformed into a different signal after ordering policies are applied to it, forming the signal that is observed upstream and used for forecasting.
This thesis extends the bullwhip literature by studying the full distributional shape of the upstream demand signal, not only its variance. Consumer demand is modelled with a count distribution, the negative binomial, whereas it is usually modelled with continuous Gaussian or AR(1) demand. The objective is to analyse how consumer demand characteristics and retailer ordering policy jointly shape the statistical properties and distributional form of the sell-in signal.
The method used to study this is a two-echelon supply chain simulation where an order-up-to policy is applied to negative binomial consumer demand. Multiple non-linearities are also added to the ordering policy: batch rounding, minimum order quantity, and a non-negativity constraint. The simulation is run for 5 184 parameter and demand-scenario combinations, and the resulting sell-in signals are analysed using summary statistics, Spearman correlation, Morris-style sensitivity analysis, and distribution fitting using MLE with model selection based on AIC and BIC.
The results show that the dominant drivers of demand signal transformation from ordering policies are the review period and the lead time. An elevated zero proportion is a characteristic of the upstream sell-in signal compared to consumer demand. Of the tested count data distributions, Poisson-Tweedie dominates for the raw sell-in signals, but transforming the unit data to batch-count data changes the situation so that ZINB and ZIP win over Poisson-Tweedie for most runs. The batch-count transform is itself an important finding, as it reduces dispersion and removes the lattice structure that batch sizes impose, making the signal more suitable for count distributions.
Aalto Stochastics Seminar / Lasse Leskelä
Nataliia Kushnerchuk
Posets of trek polynomials for directed graphical models
Monday 07 September 2026, 14:15, M3 (M234)
When a variety V𝜑 equals the image of a polynomial map 𝜑 whose coordinate
functions are combinatorial generating polynomials (i.e. polynomials enumerating combinatorial
objects), the geometry of V𝜑 reflects identities satisfied by the generating polynomials. The
resulting interplay between combinatorics and algebraic geometry can be used to answer questions
about V𝜑 . A recent technique proposes to do so using a partially ordered set (poset) 𝑃𝜑 defined
via the coefficient vectors of the polynomials defining 𝜑.
In this talk I am going to talk about a subfamily of Gaussian directed graphical models that we have studied with this new technique.
For this family, the generating polynomials of 𝜑 defining a graphical model enumerate certain subgraphs known as
treks. We characterized the poset 𝑃𝜑, and used the characterization to compute the linear span of V𝜑 , prove it is toric and deduce
a basis for its vanishing ideal. As an additional consequence, it is shown that the varieties for two distinct directed
trees intersect in a strictly lower-dimensional variety. This solves an instance of the structural
identifiability problem in the graphical models program from statistics.
Based on https://arxiv.org/abs/2608.08325
AGC Seminar
Jesse Piispanen
On well-rounded lattices and theta function minimization (MSc thesis presentation)
Thursday 10 September 2026, 14:15, M3 (M234)
Advisor: Max Forst, Supervisor: Camilla Hollanti
ANTA Seminar / Hollanti et al.
Lorenzo Zacchini (Aalto University)
TBA (midterm review)
Wednesday 23 September 2026, 10:15, M3 (M234)
Analysis seminar / Hytönen
Henri Lahdelma
Midterm review talk
Wednesday 21 October 2026, 10:15, M2 (M233)
Seminar on analysis and geometry
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