Conference Agenda
Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).
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Session Overview | |
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Location: vonRoll, Fabrikstr. 6, 001 468 seats, 433 m^2 |
| Date: Tuesday, 09/Jul/2019 | |
| 8:15am - 8:30am | Opening by the Chairs and word of welcome by Daniel Candinas, Vice-Rector for Research, University of Bern |
| vonRoll, Fabrikstr. 6, 001 | |
| 8:30am - 9:30am | IP01: Pablo A. Parrilo: Switched linear systems and infinite products of matrices |
| vonRoll, Fabrikstr. 6, 001 | |
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8:30am - 9:30am
Switched linear systems and infinite products of matrices Massachusetts Institute of Technology, United States of America Many situations of interest can be modeled as "switched linear systems", which are collections of linear difference equations, with some logical rule for switching between subsystems. Mathematically, this boils down to understanding infinite products of matrices, all of which are elements of a given finite set. Analyzing these systems is a difficult question that appears in a number of applications, including the analysis of optimization algorithms, information theory, and wavelets. Depending on whether the switching is deterministic or stochastic, different notions can be used to quantify the resulting convergence rate, like the joint spectral radius, or the Lyapunov exponent. In this talk, we provide a gentle introduction to this class of problems, their applications, and several results regarding their exact and approximate computation. |
| 1:30pm - 2:30pm | IP02: Tamara G. Kolda: Efficient Computation of Low-Rank Approximations to Higher-Order Moments |
| vonRoll, Fabrikstr. 6, 001 | |
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1:30pm - 2:30pm
Efficient Computation of Low-Rank Approximations to Higher-Order Moments Sandia National Laboratories, United States of America We consider the problem of decomposing a data tensor that is naturally expressed as the sum of p symmetric outer products of vectors of length n. For instance, a dth-order empirical moment tensor has such an expression, and there have been examples of this structure arising in machine learning problems. Our goal is to find the best approximate decomposition that is the sum of r symmetric outer products with r « p. We reduce the work and storage from exponential to linear in n, breaking the curse of dimensionality. When p is massive or the data is streaming, we show that stochastic sampling methods can be used to further reduce the complexity. We also show some intriguing finding on the rank of random tensors. This is joint work with PhD candidate Samantha Sherman at the University of Notre Dame. |
| Date: Wednesday, 10/Jul/2019 | |
| 8:25am - 8:30am | Announcements |
| vonRoll, Fabrikstr. 6, 001 | |
| 8:30am - 9:30am | IP03: Lauren K. Williams: Cluster algebras and applications to geometry |
| vonRoll, Fabrikstr. 6, 001 | |
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8:30am - 9:30am
Cluster algebras and applications to geometry Harvard University, United States of America Cluster algebras are a class of commutative rings with a remarkable combinatorial structure, which were introduced by Fomin and Zelevinsky around 2000. I will give a gentle introduction to cluster algebras, and then explain how Grassmannians and more generally their Schubert varieties have a cluster algebra structure (joint work with Khrystyna Serhiyenko and Melissa Sherman-Bennett). If time permits, I will also discuss applications to toric degenerations and mirror symmetry (joint work with Konstanze Rietsch). |
| 1:30pm - 2:30pm | IP04: Helmut Pottman: Applications of sphere geometries in computational design |
| vonRoll, Fabrikstr. 6, 001 | |
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1:30pm - 2:30pm
Applications of sphere geometries in computational design KAUST, Saudi Arabia The classical sphere geometries of Möbius, Laguerre and Lie provide a rich source of knowledge which can be highly useful in the solution of problems in computational design. We will demonstrate this at hand of three application scenarios which also exhibit a relation to algebraic geometry: (i) Rational curves and surfaces with rational offsets possess various applications in Computer-Aided Manufacturing. Their study and design can be based on Laguerre geometry, where they appear as unconstrained rational curves or surfaces in the so-called isotropic model. (ii) The most elegant discrete versions of principal curvature parameterizations of surfaces are objects of sphere geometries and they form the basis for the construction of smooth surfaces from low degree algebraic patches. (iii) The design of various types of circle patterns on surfaces can be effectively based on sphere geometric models. These patterns only exist on those surfaces which carry at least two families of circles. Their complete classification is a problem of algebraic geometry which has been recently solved by R. Krasauskas and M. Skopenkov. |
| 5:15pm - 6:00pm | SI(AG)^2 Early Career Prize Lecture: Elina Robeva: Orthogonal Tensor Decomposition |
| vonRoll, Fabrikstr. 6, 001 | |
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Orthogonal Tensor Decomposition Massachusetts Institute of Technology, United States of America Tensor decomposition has many applications. However, it is often a hard problem. In this talk we will discuss a family of tensors, called orthogonally decomposable, which retain some of the properties of matrices that general tensors don't. A symmetric tensor is orthogonally decomposable if it can be written as a linear combination of tensor powers of n orthonormal vectors. As opposed to general tensors, such tensors can be decomposed efficiently. We study the spectral properties of symmetric orthogonally decomposable tensors and give a formula for all of their eigenvectors. We also give polynomial equations defining the set of all such tensors. Analogously, we study nonsymmetric orthogonally decomposable tensors, describing their singular vector tuples and giving polynomial equations that define them. To extend the definition to a larger set of tensors, we define tight-frame decomposable tensors and study their properties. Finally, we conclude with some open questions and future research directions. |
| Date: Thursday, 11/Jul/2019 | |
| 8:25am - 8:30am | Announcements |
| vonRoll, Fabrikstr. 6, 001 | |
| 8:30am - 9:30am | IP05: Alicia Dickenstein: Algebra and geometry in the study of enzymatic cascades |
| vonRoll, Fabrikstr. 6, 001 | |
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8:30am - 9:30am
Algebra and geometry in the study of enzymatic cascades Universidad de Buenos Aires, Argentine Republic In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible. |
| 1:30pm - 2:30pm | IP06: Jonas Peters: Data Science and Causality |
| vonRoll, Fabrikstr. 6, 001 | |
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1:30pm - 2:30pm
Data Science and Causality University of Copenhagen, Denmark In data science, we are used to infer models that predict the observed data as well as possible. In causality, we try to understand how a system reacts under interventions, e.g., in gene knock-out experiments. Bringing together data science and causality may yield two benefits. (1) One may try to learn causal models from observations, and (2) enhancing standard regression or classification techniques with causal ideas may yield models that generalize better to unseen experiments. In this talk, we introduce the concept of causality, discuss ideas for addressing the above goals, and mention open problems that could benefit from an algebraic geometry point of view. No prior knowledge about causality is required. |
| Date: Friday, 12/Jul/2019 | |
| 8:25am - 8:30am | Announcements |
| vonRoll, Fabrikstr. 6, 001 | |
| 8:30am - 9:30am | IP07: Kristin Lauter: Supersingular Isogeny Graphs in Cryptography |
| vonRoll, Fabrikstr. 6, 001 | |
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8:30am - 9:30am
Supersingular Isogeny Graphs in Cryptography Microsoft Research, United States of America As we move towards a world where quantum computers can be built at scale, we are forced to consider the question of what hard problems in mathematics our next generation of cryptographic systems will be based on. Supersingular Isogeny Graphs were proposed for use in cryptography in 2006 by Charles, Goren, and Lauter. Supersingular Isogeny Graphs are examples of Ramanujan graphs, which are optimal expander graphs. These graphs have the property that relatively short walks on the graph approximate the uniform distribution, and for this reason, walks on expander graphs are often used as a good source of randomness in computer science. But the reason these graphs are important for cryptography is that finding paths in these graphs, i.e. routing, is hard: there are no known subexponential algorithms to solve this problem, either classically or on a quantum computer. For this reason, cryptosystems based on the hardness of problems on Supersingular Isogeny Graphs are currently under consideration for standardization in the NIST Post-Quantum Cryptography (PQC) Competition, and have advanced to the second round of the competition. This talk will introduce these graphs, the cryptographic applications, and the various algorithmic approaches which have been tried to attack these systems. |
| 1:30pm - 2:30pm | IP08: Jeremy Gunawardena: Some mathematical aspects of gene regulation |
| vonRoll, Fabrikstr. 6, 001 | |
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1:30pm - 2:30pm
Some mathematical aspects of gene regulation Harvard Medical School, United States of America The “linear framework” describes biochemical systems under timescale separation in terms of a finite directed graph with labelled edges. When applied to gene regulation, the framework gives a gene's input-output response as a rational function of the graph labels. The sharpness of the response, or the sensitivity of output to changes in inputs, is important for understanding how gene-regulatory mechanisms control the the development of the organism during ontogeny as well as how such mechanisms evolve during phylogeny. We outline some mathematical problems relating to the sharpness of genetic input-output responses, with a focus on the role of energy expenditure away from thermodynamic equilibrium. |
| 5:15pm - 7:00pm | SI(AG)^2 business meeting |
| vonRoll, Fabrikstr. 6, 001 | |
| Date: Saturday, 13/Jul/2019 | |
| 8:25am - 8:30am | Announcements |
| vonRoll, Fabrikstr. 6, 001 | |
| 8:30am - 9:30am | IP09: Mauricio Velasco: Extremal properties of 2-regular varieties |
| vonRoll, Fabrikstr. 6, 001 | |
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8:30am - 9:30am
Extremal properties of 2-regular varieties Universidad de los Andes, Colombia A projective variety is called two regular if it is defined by quadrics and all matrices in the minimal free resolutions of its homogeneous coordinate ring have linear entries. In an objective sense these are "the simplest" projective varieties and perhaps for this very reason they are ubiquitous in algebraic geometry. In this talk I will explain several novel contexts of interest for the SIAGA community where these varieties play a prominent role. In the process we will describe other properties which characterize two-regular varieties highlighting the fruitful interplay between classical and convex algebraic geometry. |
| 1:30pm - 2:30pm | IP10: Kathryn Hess Bellwald: Topological adventures in neuroscience |
| vonRoll, Fabrikstr. 6, 001 | |
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1:30pm - 2:30pm
Topological adventures in neuroscience EPFL, Switzerland Over the past decade, and particularly over the past five years, research at the interface of topology and neuroscience has grown remarkably fast. Topology has, for example, been successfully applied to objective classification of neuron morphologies and to automatic detection of network dynamics. In this talk I will focus on the algebraic topology of brain structure and function, describing results obtained by members of my lab in collaboration with the Blue Brain Project on digitally reconstructed microcircuits of neurons in the rat cortex. In particular, I will describe our on-going work on the topology of synaptic plasticity. The talk will include an overview of the Blue Brain Project and a brief introduction to the topological tools that we use. |
