| Suhan Zhong | |
Polynomial lower approximations for two-stage stochastic optimization |
| Abstract:
It is a challenging problem to find global optimal solutions of nonconvex two-stage stochastic programs. We propose to find an efficient
polynomial lower bound function of the recourse function and solve the two-stage stochastic program as polynomial optimization. Such
polynomial lower bound functions can be solved by linear conic optimization.
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| Yeqiu Wang | |
Ample cones of K3 surfaces with higher dimensional generalizations |
| Abstract:
This poster discusses ample cones of K3 surfaces, their Hilbert schemes, and birational modifications.
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| Michail Savvas | |
Moduli spaces in derived geometry |
| Abstract:
Constructing moduli spaces has been a fundamental endeavor within algebraic geometry (and beyond), motivating, among
other things, the development of Geometric Invariant Theory in the 1960s and the more general theory of good moduli
spaces in the 2000s.
This poster presents how the theory extends to the setting of derived algebraic geometry, leading to natural derived
enhancements of constructions and structural results for classical moduli spaces.
It is based on joint work with Eric Ahlqvist, Jeroen Hekking, and Michele Pernice.
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| Filip Rupniewski | |
Relation between subrank and border subrank |
| Abstract:
To measure tensor complexity, multiple notions of ranks were introduced, such as tensor rank and subrank.
Tensors with a high value (subrank) and low cost (tensor rank) are very desirable.
They are used (in laser method) to construct the fastest algorithms for matrix multiplication.
The poster discusses the relationship between subrank and its border version, as well as their various properties such as the
non-additivity of (border) subrank and the growth rate of generic (border) subrank.
Based on the joint work with Benjamin Biaggi, Chia-Yu Chang and Jan Draisma
(https://arxiv.org/abs/2402.10674).
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| Jonah Robinson | |
Invariants of the Dispersion Relation for Discrete Periodic Operators |
| Abstract:
We utilize tools of computational algebraic geometry to study the dispersion relation for discrete Schrödinger operators with
generic
parameters on various periodic graphs, with the goal of better understanding the geometry of critical points of the Bloch variety.
In pursuit of this goal we study various invariants of the dispersion relation; such as Newton polytope, singular and degenerate loci,
and the singular loci of its facial systems.
Our investigations were carried out using Macaulay2 and the Texas A&M Mathematics department's computational cluster, Whistler,
enabling us to harvest data for all small graphs with various fixed supports.
We present various phenomena observed in this study as well as several conjectures arising from these observations.
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| Tomasz Mandziuk | |
Multigraded Hilbert schemes of points in general position |
| Abstract:
Given a product of projective spaces X and a positive integer r we consider the parameter space of homogeneous ideals
in the coordinate ring of X that have the same Hilbert function as r points in general position in X.
We classify for which X and r the parameter space is irreducible.
The work is motivated by border apolarity which establishes a connection between a distinguished irreducible
component of the parameter space that we consider and the notion of border rank.
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| Gari Lincoln Chua | |
On Stability and Denominators of F-pure Thresholds in Families of Diagonal Hypersurfaces |
| Abstract:
The F-pure threshold of a polynomial f of characteristic p> 0 is an invariant of the singularities of f,
with smaller values corresponding to worse singularities.
In many cases, the F-pure threshold is a rational number, and questions about the denominator of the F-pure threshold
have been asked.
In this poster, we investigate a family of polynomials whose F-pure thresholds stabilize for some primes and whose prime power
in the denominators is unbounded.
In particular, given any prime p, we can find a family of polynomials such that their F-pure thresholds are powers
of p, with no uniform bound on the power appearing in the denominator.
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