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Date Time |
Location | Speaker |
Title – click for abstract |
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01/27 3:00pm |
BLOC 302 |
JM Landsberg Texas A&M |
The cheapest tensors
Motivated by quantum information theory and the complexity of matrix multiplication, one would like to classify tensors of "minimal border rank".
This is now understood to be a difficult problem with deep connections to algebraic geometry and commutative algebra.
After giving an introduction to the topic with motivation and basic definitions, I will describe recent progress on the question, in particular the introduction of "atomic tensors". This is joint work in progress with J. Jelisiejew and T. Mandziuk. |
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01/31 5:00pm |
BLOC 302 |
M. Varbaro |
Singularities of Herzog varieties
Let S be a polynomial ring over a field and I a homogeneous ideal. We say that I as a Herzog ideal if there exists a monomial order < on S such that in_<(I) is squarefree. A projective variety X is a Herzog variety if it admits an embedding in which it is defined by a Herzog ideal.
If X is a Herzog variety with respect to a revlex order, with Constantinescu and DeNegri we proved that the smoothness of X forces S/I to be Cohen-Macaulay with negative a-invariant (hence a (F)-rational singularity). We will discuss the problem wether this happens for any Herzog variety (not necessarily w.r.t. a revlex order); this is not even clear when X is a curve. In this case, rephrasing the problem the question is:
if X is a Herzog smooth projective curve, does X have genus 0?
In this talk we will largely discuss this problem, giving some evidence for it and explaining why it is difficult to show it in general, giving insights on an ongoing work with Amy Huang, Jonah Tarasova and Emily Witt. |
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02/01 09:00am |
BLOC 302 |
multiple speakers |
Symmetries and Singularities in Texas conference
See
https://people.tamu.edu/~jml//symmetries-texas%203/main.html
and please register if you plan to attend any of the talks.
The conference will continue Sunday morning as well. |
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02/10 3:00pm |
BLOC 302 |
S. Lovett UCSD |
Corners and arithmetic extensions of Kelley-Meka
A classical question in additive combinatorics, dating back for close to 100 years, is what is the densest subset of integers without a 3-term arithmetic progression. In 2023, Kelley and Meka made a huge breakthrough on the problem, proving bounds which are close to the best known constructions. In this talk, I will describe an on-going effort to extend their techniques to more problems in additive combinatorics, and in particular to the "corners" problem, which can be viewed as a 2-dimensional analog of the 3-term arithmetic progression problem, and variants of it.
Joint work with Michael Jaber and Anthoni Ostuni. |
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02/17 3:00pm |
BLOC 302 |
K. Sivic |
Irreducible components of Hilbert schemes of points
Hilbert schemes of points in affine spaces parameterize artinian algebras of given length. In the talk we classify irreducible components of Hilbert schemes of 9 and 10 points in affine spaces of any dimension. The main tool is the connection between Hilbert schemes of points and varieties of commuting matrices. This is joint work with Maciej Gałązka and Hanieh Keneshlou.
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02/24 3:00pm |
BLOC 602 |
Thomas Yahl University of Wisconsin |
TBA |
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03/03 3:00pm |
BLOC 302 |
R. Oliveira U. Waterloo |
Primes via Zeros: interactive proofs for testing primality of natural classes of ideals
A central question in mathematics and computer science is the question of determining whether a given ideal I is prime, which geometrically corresponds to the zero set of $I$, denoted $Z(I)$, being irreducible.
The current best algorithms for the ideal primality testing problem require, in the worst-case, exponential space (i.e., in EXPSPACE).
This state of affairs has prompted intense research on the computational complexity of this problem even for special and natural classes of ideals.
Notable classes of ideals are the class of radical ideals, complete intersections (and more generally Cohen-Macaulay ideals).
For radical ideals, the current best upper bounds are given by (Buergisser & Scheiblechner, 2009), putting the problem in PSPACE.
For complete intersections, the primary decomposition algorithm of (Eisenbud, Huneke, Vasconcelos 1992) coupled with the degree bounds of (Dickenstein et al 1991), puts the ideal primality testing problem in exponential time (EXP).
In these situations, the only known complexity-theoretic lower bound for the ideal primality testing problem is that it is coNP-hard for the classes of radical ideals, and equidimensional Cohen-Macaulay ideals.
In this work, we significantly reduce the complexity-theoretic gap for the ideal primality testing problem for the important families of ideals (namely, *radical ideals* and *equidimensional Cohen-Macaulay ideals*).
For these classes of ideals, assuming the Generalized Riemann Hypothesis, we show that primality testing can be efficiently verified (also by randomized algorithms).
This significantly improves the upper bound for these classes, approaching their lower bound, as the primality testing problem is coNP-hard for these classes of ideals.
This talked is based on joint work with Abhibhav Garg and Nitin Saxena. |
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03/21 4:00pm |
BLOC 302 |
Demetre Kazaras Michigan State University |
TBA |
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03/24 3:00pm |
BLOC 302 |
Tianyi Yu UQAM |
TBA |
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04/11 4:00pm |
BLOC 302 |
K. Ganapathy U. Michigan |
TBA |
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04/14 3:00pm |
BLOC 302 |
J. Wilson Colorado State |
DETECTING CLUSTER PATTERNS IN TENSOR DATA USING LIE THEORY
I'll introduce a class of cluster patterns for tensor data used in
pattern matching, outlier detections, statistics and signal processing. Then I will show
they are all shadows of a general pattern detected efficiently by algebra, specifically Lie theory.
It is a direction with many open problems, some about theory, others about applied improvements.
Reports on joint work with Brooksbank and Kassabov.
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