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Monday

8:00 - 8:45 Registration
The registration desk is open throughout the week.
8:45 - 9:00 Opening Remarks (CLC013)
Organizing Committee
9:00-10:00 Plenary 1 (CLC013): Tropical Graph Embeddings
Josef Schicho (Johannes Kepler University Linz, Austria)
Abstract Let \(G=(V,E)\) be a simple, undirected graph without self-loops and let \(\lambda\in\mathbb R^{E}\) be a labeling of edges by real numbers. A planar framework of \((G,\lambda)\) is a function \(\rho\) mapping \(V\) into the plane such that the squared Euclidean distance between vertices connected by an edge is equal to the label of that edge. If we say the plane is \(\mathbb R^2\), and the squared distance is given by a nondegenerate quadratic form, then the set of planar frameworks is an algebraic variety. For generic labeling, its dimension is \(2|V|-|E|\), if not empty.
The group \(\mathrm{SE}_2\) of Euclidean displacements acts on the variety of frameworks. To choose representatives, we pass to "pinned frameworks", which have one edge fixed. The dimension drops then by \(3\) to \(2|V|-|E|-3\). In this talk, we will ask several questions about the algebraic variety of pinned frameworks, in dimension 0 and 1, and try to answer them by tropical geometry.
With tropical geometry, one can take an algebraic variety and "tropicalise" it, obtaining a piecewise linear object that reflects some properties of the algebraic variety. Instead of costly algebraic computations, we will answer our questions by faster combinatoric algorithms.
10:00-10:30 Coffee Break (CLC402 and CLC403)
10:30-12:00 Parallel Session 1 (CLC202 [left] and CLC203 [right])
Computational and Effective Commutative Algebra Real Projective Geometry and Grassmannian
  • Barbara Betti*, Viktoriia Borovik:
    The SagbiHomotopy.jl package for solving polynomial systems
  • Viktoriia Borovik, Hannah Friedman, Serkan Hosten, Max Pfeffer:
    Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties
  • Kisun Lee*:
    A priori bounds for certified Krawczyk homotopy tracking
  • Josué Tonelli-Cueto*:
    Condition-based Low-Degree Approximation of Real Polynomial Systems. II.W: The Positive Dimensional Case in the Elliptic Regime
  • Benjamin Hollering*, Elia Mazzucchelli, Matteo Parisi, Bernd Sturmfels:
    Varieties of Lines in 3-Space
  • Alheydis Geiger*, Francesca Zaffalon:
    The Self-Projecting Grassmannian
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    12:00-14:00 Lunch (CLC402 and CLC403)
    14:00-15:00 Plenary 2 (CLC013): Symmetric Ideals
    Alexandra Seceleanu (University of Nebraska-Lincoln. USA)
    Abstract An ideal in a polynomial ring is called symmetric if it is invariant as a set under the action of the symmetric group, which permutes variables. This talk explores two classes of symmetric ideals: those reflecting the typical behavior of a randomly chosen symmetric ideal, and those enriched with strong combinatorial structure arising from the Borel group.
    In the first part, motivated by the principle that a general member in a family often exhibits desirable properties, we develop a framework for defining and studying general symmetric ideals with a fixed number of generators up to symmetry. This perspective reveals interesting homological stability phenomena.
    In the second part, focusing on symmetric ideals generated by monomials, we introduce the notion of symmetric strongly sifted ideals - the symmetrizations of strongly stable ideals from commutative algebra. We present structural, homological, and combinatorial results for the former ideals, highlighting their connections to discrete polymatroids and permutohedral toric varieties.
    This talk is based on joint work with Megumi Harada and Liana Sega, as well as separate collaborations with Liana Sega and Alessandra Costantini.
    15:00-15:30 Coffee Break (CLC402 and CLC403)
    15:30-17:00 Parallel Session 2 (CLC202 [left] and CLC203 [right])
    Computational and Effective Commutative Algebra Real Projective Geometry and Grassmannian
  • Johannes Schmitt*:
    Homogeneous Khovanskii bases and MUVAK bases
  • Filip Jonsson Kling, Samuel Lundqvist, Fatemeh Mohammadi, Matthias Orth*:
    The Gröbner basis for powers of a general linear form in a monomial complete intersection
  • Joshua Grochow, Abhiram Natarajan:
    Gröbner bases native to term-ordered commutative algebras, with application to the Hodge algebra of minors
  • Cordian Riener, Ettore Teixeira Turatti*:
    Quadrature rules with few nodes supported on algebraic curves
  • Julian Weigert*, Clemens Brüser:
    Geometry of Adjoint Hypersurfaces for Polytopes
  • Teresa Cortadellas, Carlos D'Andrea*, Ana Belen de Felipe, Joel Hurtado Moreno, M. Eulalia Montoro:
    On the effective Pourchet's Theorem
    		•

    Tuesday

    9:00-10:00 Plenary 3 (CLC013): On strongly robust toric ideals
    Dimitra Kosta (University of Edinburgh, UK)
    Abstract A toric ideal is called strongly robust when its minimal system of generators coincides with its Graver basis. In the talk, I will explain how using the bouquet structure one can build a strongly robust simplicial complex which determines the strongly robust property of toric ideals. This turns Sullivant's question about the structure of the bouquets of strongly robust toric ideals, into a question about the dimension of the strongly robust simplicial complex. I will then discuss our results on the strongly robust property which include the case of monomial curves, codimension 2 toric ideals and configurations in general position. This is joint work with A. Thoma and M. Vladoiu.
    10:00-10:30 Coffee Break (CLC402 and CLC403)
    10:30-12:00 Parallel Session 3 (CLC202 [left] and CLC203 [right])
    Algebraic Statistics, Models, Identifiability Positivity, Real Algebraic Geometry, Polynomial Optimization
  • Roser Homs, Danai Deligeorgaki, Bryson Kagy, Aida Maraj, Joseph Johnson:
    Maximum likelihood thresholds vs generic completion rank in colored gaussian graphical models
  • Jane Ivy Coons, Nataliia Kushnerchuk, Jiayi Li, Sarah Lumpp, Janike Oldekop, Cecilie Olesen Recke*, Elina Robeva:
    Identifiability in Non-Gaussian Discrete Lyapunov Models
  • Eliana Duarte, Bernhard Reinke*, Federico Lazzeri, Ludovico Piazza, Bowen Li, Nico Wolf:
    MLdegrees of 3D polytopes with MLdegree one faces
    		•
  • Lorenzo Baldi, Rainer Sinn, Máté L. Telek, Julian Weigert*:
     Toric Extensions of Pólya's Theorem
  • Elisenda Feliu, Joan Ferrer, Máté L. Telek:
    Copositivity, discriminants and nonseparable signed supports
  • Matías Bender, Khazhgali Kozhasov, Elias Tsigaridas, Chaoping Zhu:
    Certificates for nonnegativity of multivariate integer polynomials under perturbations
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    12:00-14:00 Lunch (CLC402 and CLC403)
    14:00-15:00 Plenary 4 (CLC013): On the distance to singular hypersurfaces
    Khazhgali Kozhasov (Université Côte d'Azur, France)
    Abstract The Euclidean Distance degree of an affine (real) algebraic variety X is (an upper bound on) the number of (real) critical points of the Euclidean distance to X from a generic (real) point u. However, if X is singular, a minimizer might belong to the singular locus of X for a positive-dimensional set of inputs u and thus it is natural to study the Euclidean distance to Sing(X). I will discuss this phenomenon for the discriminant X=D consisting of degree d (real) homogeneous polynomials with (real) singular points, where the ambient space is endowed with the Bombieri (also known as Fubini-Study) Euclidean structure. I will present a formula for the ED degree of the component of Sing(D) that contains polynomials with cuspidal singularities. This, together with the known formula for the ED degree of D, gives a measure of algebraic complexity of the distance minimization problem to D. The talk is based on a joint work with B. Mourrain and A. Parusiński.
    15:00-15:30 Coffee Break (CLC402 and CLC403)
    15:30-17:10 Software presentations (CLC013)
  • Anne Fruehbis-Krueger, Michael Joswig, Lars Kastner*
    Drawing real plane algebraic curves in OSCAR
  • Gabriel Riffo, Leonard Schmitz*
    Signature Tensors in OSCAR
  • Zoltán Kovács, Alvaro Nolla, Tomás Recio, M. Pilar Vélez
    The ShowProof command in GeoGebra: automated ranking and derivation of geometric statements
  • Paul Breiding, John Cobb, Aviva Englander, Nayda Farnsworth, Jonathan Hauenstein, Oskar Henriksson*, David Johnson, Jordy Lopez Garcia, Deepak Mundayur
    Numerical elimination with ProjectedHypersurfaces.jl
  • Timothy Duff, Viktor Korotynskiy, Anton Leykin*, Tomas Pajdla
    Computer-Assisted Discovery and Proofs of Compatibility Conditions for Three Projective Cameras
    • 17:10-20:00 Poster Session (CLC402 and CLC403)
    Catering (food and drinks) will be provided.

    Wednesday

    9:00-10:00 Plenary 5 (CLC013): Multi-context principal component analysis
    Anna Seigal (Harvard University, USA)
    Abstract Tensor decomposition seeks to recover factors in multi-dimensional arrays. I’ll present a new algorithm for decomposing tensors called the multi-subspace power method. It recovers a decomposition one summand at a time using the higher-order power method. Finding summands one by one is beneficial for accuracy and interpretability, but is known to fail in general. The approach overcomes this problem by transforming the input tensor to one with orthonormal slices, via change of basis. Tensor decomposition enables the comparison of variables across contexts (for example, patients across diseases or words across genres). We use our algorithm for multi-context principal component analysis (MCPCA), a tool to find axes of variation shared across subsets of contexts. Just as usual principal component analysis is a low-rank approximation of the covariance matrix, MCPCA finds a low rank approximation of the third-order tensor obtained by stacking covariance matrices across contexts. I’ll describe its applications to study gene expression across disease types and contextualized word embeddings across genres of text. Based on joint work with Kexin Wang, Salil Bhate, João Pereira, Joe Kileel, and Matylda Figlerowicz. 
    10:00-10:30 Coffee Break (CLC402 and CLC403)
    10:30-12:00 Parallel Session 4 (CLC202 [left] and CLC203 [right])
    Tensor Decompositions and Ranks Applied Algebraic Geometry, Dynamical Systems Signatures
  • Alessandra Bernardi, Oriol Reig Fité*:
    A refinement on the local cactus rank algorithm
  • Enrica Barrilli*, Bernard Mourrain, Daniele Taufer:
    Generalized Additive Decompositions of Symmetric Tensors
  • Tim Seynnaeve*, Daniele Taufer, Nick Vannieuwenhoven:
    Chisel-based tensor decomposition
    		•
  • Francesco Maria Mascarin, Simon Telen:
    Lissajous Varieties
  • Francesco Galuppi, Giovanni Moreno, Pierpaola Santarsiero*:
    Path signatures of ODE solutions
  • Flavio Salizzoni, Luca Sodomaco*, Julian Weigert:
    Nonlinear Kalman varieties
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    12:00-14:00 Lunch (CLC402 and CLC403)
    14:00- Free afternoon

    There will be a hike through South Durham and along the River Wear, the total route is around 15km with a few small hills. For those who prefer a shorter route, the first 2km takes us along a road to the Low Burnhall nature reserve. Please join us for that and explore the nature reserve, then turn back towards John Snow college or the city centre; there are also regular busses (number 6) from the nature reserve back up the road that go to the centre.

    Thursday

    9:00-10:00 Plenary 6 (CLC013): Vertically parametrized systems and the generic geometry of steady state varieties of reaction networks
    Elisenda Feliu (University of Copenhagen, Denmark)
    Abstract The mathematical theory of chemical and biochemical reaction networks traces its origins to the pioneering work of Feinberg, Horn, and Jackson in the 1970s. Despite substantial progress, several fundamental questions concerning the positive steady states of reaction networks remain open. These steady states are described by a parametric polynomial system with a special structure known as a "vertically parametrized system". Recent advances have revealed a rich geometric framework for vertically parametrized systems, extending many classical results for sparse (or freely parametrized) polynomial systems with fixed support.
    In this talk, I will present some of these developments and highlight their implications for reaction network theory. Among the topics discussed will be generic finiteness and nondegeneracy of steady states, toric structures, absolute concentration robustness, and the nondegenerate multistationarity conjecture. This is joint work with Oskar Henriksson and Beatriz Pascual Escudero.
    10:00-10:30 Coffee Break (CLC402 and CLC403)
    10:30-12:00 Parallel Session 5 (CLC202 [left] and CLC203 [right])
    Statistics, Models, Applications Combinatoric and Toric Algebra
  • Mathias Drton, Elizabeth Gross, Dimitra Kosta, Anton Leykin, Seth Sullivant, Daniel Windisch*:
    Singular Learning Theory for Factor Analysis
  • Benjamin Biaggi, Jan Draisma, Fulvio Gesmundo, Aida Maraj, Magdaléna Misinová*:
    Computing The Continuous Symmetries of a Parametrized Variety
  • Rodica-Andreea Dinu, Martin Vodicka:
    Proof of a Conjecture of Drton, Sturmfels and Sullivant on the maximum likelihood degree of the Gaussian graphical model of a cycle
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  • Dario Antolini*, Sean Dewar, Shin-Ichi Tanigawa:
    Dilworth truncations and Hadamard products of linear spaces
  • Andreas Gross, Kevin Kühn*, Dante Luber:
    Minuscule Coxeter Dressians
  • Stefano Canino*, Alex Casarotti, Pierpaola Santarsiero:
    A new bound on the rank of tensor product of W-states
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    12:00-12:10 Group picture (in front of building)
    12:00-14:00 Lunch (CLC402 and CLC403)
    14:00-15:00 Plenary 7 (CLC013): Polynomial Constraint Extraction Techniques in the Graphical Models Program
    Liam Solus (KTH Royal Institute of Technology, Sweden)
    Abstract Applied algebra is driven in large part by the realization that many models for real data can be viewed as semialgebraic sets parameterized via a rational map. An important example are graphical models, which provide a flexible framework for developing statistical inference techniques for multivariate data.  Since data comes in many shapes and sizes, different graphical model families are needed for different data problems, and each family requires its own basic mathematical theory to support inference. In this context, general techniques for recovering implicit (polynomial) constraints satisfied by semialgebraic sets translate into tools for developing the basic theory of graphical model families.  In this talk, we will discuss the connection between the graphical models program and the research program in applied algebra centered on extracting polynomial constraints satisfied by parametrized semialgebraic sets. Special attention will be given to some recent polynomial constraint extraction techniques that offer solutions in the graphical models program where no non-algebraic solution exists.
    15:00-15:30 Coffee Break (CLC402 and CLC403)
    15:30-17:00 Parallel Session 6 (CLC202 [left] and CLC203 [right])
    Statistics, Models, Applications Combinatoric and Toric Algebra
  • Elizabeth Pratt, Kexin Wang:
    Avoidance Loci of Real Projective Varieties
  • Cosimo Flavi*, Fulvio Gesmundo, Alessandro Oneto, Emanuele Ventura:
    Polynomials of small slice rank and strength
  • Niels Lubbes*:
    Webs on pointwise sums of two rational curves
    		•
  • Alexander Taveira Blomenhofer, Benjamin Lovitz:
    A linear-time algorithm for Chow decompositions
  • Henri Breloer, Cordian Riener:
    The Symmetric Hilbert Series
  • Ignacio García Marco, Philippe Gimenez, Mario González-Sánchez*:
    Castelnuovo-Mumford regularity of toric varieties with at most one singular point
    		•
    17:30-19:00 Board Meeting (MCS3070)
    The board meeting is private. Only members of the advisory board and explicitely invited partipants may participate.
    19:00- Evening social @ Gray College Bar
    Drinks and snacks (no food) can be purchased at the bar.

    Friday

    9:00-10:00 Plenary 8 (CLC013): Algebraic geometry and integer lattices: Symmetries of K3 surfaces
    Tommy Hofmann (University of Siegen, Germany)
    Abstract The theory of integral quadratic forms, or equivalently integer lattices, is a classical topic in number theory. Since integer lattices arise naturally wherever a bilinear structure is present, they appear across many areas of mathematics. In this talk we survey their role in geometry, focusing on intersection forms as they arise in various geometric contexts. Our main focus is K3 surfaces, for which integer lattices yield an algorithmic approach to the classification of finite automorphism groups. This is joint work with Simon Brandhorst.
    10:00-10:30 Coffee Break (CLC402 and CLC403)
    10:30-12:00 Parallel Session 7 (CLC202 [left] and CLC203 [right])
    Effective Computation, Algorithms, Software Tensors, Complexity, Quantum-type Applications
  • Daniel Holmes*, Giosuè Muratore:
    Effective computation of Gromov-Witten invariants for GKM spaces
  • Christiane Ott*:
    Algorithms to Calculate Invariant Rings of Finite Group Schemes
  • Hirotachi Abo, Kristian Ranestad, Frank-Olaf Schreyer:
    Nongeneral-type surfaces in projective four-space: a package for Macaulay2
    		•
  • Maxim van den Berg*, Matthias Christandl, Vladimir Lysikov, Harold Nieuwboer, Michael Walter, Jeroen Zuiddam:
    Computing moment polytopes of tensors and polynomials
  • Paolo Andreini, Alessandra Bernardi, Barbara Toniella Corradini, Sara Marziali*, Giacomo Nunziati, Franco Scarselli:
    Neural Learning of Fast Matrix Multiplication Algorithms: A StrassenNet Approach
  • Elke Neuhaus*, Irem Portakal, Vincenzo Galgano, Fabian Faulstich:
    The Coupled Cluster Doubles Truncation Variety of Four Electrons
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    12:00-14:00 Lunch (CLC402 and CLC403)
    14:00-15:00 Plenary 9 (CLC013): Tensors and hidden symmetries
    Michael Walter (LMU Munich, Germany)
    Abstract Many mathematical and computational problems have underlying (and often hidden) symmetries. Revealing these symmetries can be an essential tool for finding effective algorithms and obtaining new structural insight. I will give a gentle introduction to these connections, survey recent developments and applications (motivated by tensors, from invariant theory and statistics all the way to complexity and quantum information), and sketch how the geometric viewpoint of convex optimization on curved spaces (arising from symmetries) has recently led to significant progress.