Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsSeminar 217, Risk Management: Sustainable Responsible Investing and the Cross-Section of Return and Risk, Feb 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122088&date=2019-02-19
The identification of factors that predict the cross-section of stock returns has been a focus of asset pricing theory for decades. We address this challenging problem for both equity performance and risk, the latter through the maximum drawdown measure. We test a variety of regression-based models used in the field of supervised learning including penalized linear regression, tree-based models, and neural networks. Using empirical data in the US market from January 1980 to June 2018, we find that a number of firm characteristics succeed in explaining the cross-sectional variation of active returns and maximum drawdown, and that the latter has substantially better predictability. Non-linear models materially add to the predictive power of linear models. Finally, environmental, social, and governance impact enhances predictive power for non-linear models when the number of variables is reduced.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122088&date=2019-02-19CANCELED: Representation Theory and Mathematical Physics Seminar, Feb 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123907&date=2019-02-19
We define the action of infinitely generated Temperley-Lieb algebra on the category of representations of the supergroup \(P(n)\). The supergroup in question is an interesting super analogue of the orthogonal and symplectic groups. As an application of this construction we get algorithm computing characters of irreducible representation of \(P(n)\) and some other esults. As n tends to infinity, we obtain a new universal tensor category equipped with Temperley-Lieb algebra action. In this way we obtain representation of TL in the Fock space.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123907&date=2019-02-19Bowen Lectures, Feb 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123692&date=2019-02-19
The symmetries of systems of polynomial equations can be be understood in terms of the geometry of the variety of zeroes (or solution set) of the polynomials. Roughly speaking, there are 3 kinds of geometries corresponding to positive, zero and negative curvature giving rise to 3 different kinds of symmetry groups. In this lecture, I will discuss recent advances in algebraic geometry that lead to very precise results on the structure of these symmetry groups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123692&date=2019-02-19Harmonic Analysis Seminar, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123977&date=2019-02-20
This seminar is an ongoing discussion of Guth's Fourier restriction inequality based on the method of polynomial partitioning. This week's first topic will be a proof of basic properties of the wave packet decomposition. With this machinery in hand, we will begin the core part of the proof, introducing the key concept of broad points, indicating the role of polynomial partitioning, and formulating the inductive step.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123977&date=2019-02-20Topology Seminar (Introductory Talk), Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123354&date=2019-02-20
The Chekanov-Eliashberg algebra is a powerful Legendrian isotopy invariant that is defined by counts of pseudoholomorphic discs. We give an introduction to both analytical and algebraic aspects of the theory, perform calculations in both low and high dimension, and present some open problems.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123354&date=2019-02-20Algorithmic Pirogov-Sinai theory, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123922&date=2019-02-20
What is the connection between a phase transition in a statistical physics model and the computational complexity of sampling from the given model? In the setting of the hard-core and Potts models on lattices, it is known that in the phase coexistence regime the Glauber dynamics mix slowly. Using some of the same tools used to prove slow mixing (the cluster expansion and Pirogov-Sinai theory), we give efficient algorithms to approximate the partition function of and sample from the hard-core and Potts models at sufficiently low temperatures on the lattice. Our algorithms are inspired by Barvinok's approach to polynomial approximation. Joint work with Tyler Helmuth and Guus Regts.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123922&date=2019-02-20Number Theory Seminar, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123974&date=2019-02-20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123974&date=2019-02-20Statistics on Shape Data: Correcting an Asymptotic Bias in Template Shape Estimation, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123897&date=2019-02-20
Computational Anatomy aims to model and analyze healthy and pathological distributions of organ shapes. We are interested in the computational representation of the brain anatomy using brain MRIs (Magnetic Resonance Imaging). How can we define the notion of brain shapes and how can we learn their distribution in the population? Landmarks’ shapes, curve shapes or surface shapes can be seen as the remainder after we have filtered out the object position and orientation. As such, shape data belong to quotient spaces. We present “Geometric Statistics”, a framework for data belonging to non-Euclidean spaces like quotient spaces of Riemannian manifolds. We use tools of Geometric Statistics and Riemannian geometry to prove that the “template shape estimation” algorithm, used for more than 15 years in medical imaging (and signal processing), has an asymptotic bias. The geometric intuition provided by the study leads us to design new bias correction methods. We present experimental results on simulated and real data, including a first bias quantification of the brain template computed from MRIs.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123897&date=2019-02-20Bowen Lectures, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123693&date=2019-02-20
Algebraic varieties are geometric objects defined by polynomial equations. The minimal model program (MMP) is an ambitious program that aims to classify algebraic varieties. According to the MMP, there are 3 building blocks: Fano varieties, Calabi-Yau varieties and varieties of general type which are higher dimensional analogs of Riemann Surfaces of genus 0,1 or at least 2 respectively. In this talk I will recall the general features of the MMP and discuss recent advances in our understanding of Fano varieties and varieties of general type.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123693&date=2019-02-20Special Analysis Seminar, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123970&date=2019-02-20
Physical experiments show that interfaces between dissimilar media act as stable channels for the propagation of energy. In discrete models, this stability is explained via an index-like theorem: the bulk edge correspondence. I will first review this principle, which connects the effective number of waves propagating along the interface (a spectral invariant) to a Chern number (a topological invariant).<br />
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I will then focus on a PDE modeling conduction in a graphene layer with a line defect. In a perturbative regime, Fefferman–Lee-Thorp–Weinstein–Zhu constructed waves propagating along the defect. I will show that precisely two of them are topologically stable: they persist outside the perturbative regime. I will then calculate the associated Chern number: it is 2 or -2. These results illustrate the bulk-edge correspondence in a continuous setting.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123970&date=2019-02-20Topology Seminar (Main Talk), Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123319&date=2019-02-20
We use techniques from persistence homology applied to the Chekanov-Eliashberg algebra in order to obtain a restriction on the oscillatory norm of a contact Hamiltonian that displaces a Legendrian in the contact vector space from its image under the Reeb flow. These techniques are also used to show that a Legendrian which admits an augmentation cannot \(C^0\)-approximate a loose Legendrian, and to obstruct the existence of small positive Legendrian loops. This is joint work with M. Sullivan.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123319&date=2019-02-20Applied Math Seminar, Feb 21
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123967&date=2019-02-21
The Grassmann manifold Gr(m,n) is the set of n-dimensional subspaces in $\mathbb R^m$ (assuming m >n), and is used in many science and engineering applications. A point in Gr(m,n) can be represented by an orthogonal matrix of size m by n, multiplied by another arbitrary orthogonal matrix of size n by n. In quantum chemistry and in particular the widely used density functional theory (DFT), this arbitrary orthogonal matrix is referred to as the gauge. Physical quantities such as energies and electron densities should be independent of the gauge choice. In this talk, I am going to discuss the interplay between gauge-dependent and gauge-independent quantities in quantum chemistry along three recent directions: time-dependent density functional theory, electron localization, and self-consistent field iteration. In each case, the focus on the gauge-independent representation of the Grassmann manifold brings interesting, and sometimes surprising numerical benefits.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123967&date=2019-02-21Mathematics Department Colloquium/Bowen Lectures, Feb 21
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123694&date=2019-02-21
After recent spectacular progress in the classification of varieties over an algebraic closed field of characteristic 0 (e.g. the solution set of a system of polynomial equations defined by $p_1,...,p_r$ in $C[x_1,...,x_n]$) it is natural to try and understand the geometry of varieties defined over an algebraically closed field of characteristic $p >0$. Many technical difficulties arise in this context. Nevertheless, there has been much progress recently. In particular, the MMP was established for 3-folds in characteristic $p >5$ by work of Birkar, Hacon, Xu and others. In this talk, we will explain some of the challenges and the recent progress in this active area of research.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123694&date=2019-02-21Student Probability/PDE Seminar, Feb 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123976&date=2019-02-22
I will talk about several different perspectives to analyze the structure of Gibbs measures with low complexity. The first perspective is a mean-field approximation to the free energy that appears in the variational formula, studied by Chatterjee and Dembo. As an application, one can compute the probability of large deviation events given by nonlinear functions with low complexity, for instance counting the number of subgraphs of the Erdos-Renyi random graphs in the sparse regime. Another direction is studied by Eldan, which says that Gibbs measure is approximately close to the mixture of product measures with an error term expressed in terms of the 'Gaussian-width gradient complexity'. The another possible method is recently introduced by Austin, which is based on purely information theoretical techniques. I will briefly mention these methods and discuss the strength of each perspective and relations between them.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123976&date=2019-02-22Logic Colloquium, Feb 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123724&date=2019-02-22
The discovery of non euclidean geometry in the early nineteenth century had shaken the beliefs and conjectures of more than two thousand years and changed the picture we had for mathematics, physics and even philosophy. Lobachevsky and Bolyai independently around 1830 discovered hyperbolic geometry. A notable distinguish feature of hyperbolic geometry is its negative curvature in a way that the sum of angles of a triangle is less than π. Gromov much later in 1987 introduced hyperbolic groups which are groups acting "nicely" on hyperbolic spaces, or equivalently finitely generated groups whose Cayley graphs are "negatively curved". Main examples are free groups and almost all surface groups. The fascinating subject of hyperbolic groups touches on many mathematical disciplines such as geometric group theory, low dimensional topology and combinatorial group theory. It is connected to model theory through a question of Tarski.<br />
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Tarski asked around 1946 whether non abelian free groups have the same common first order theory. This question proved extremely hard to answer and only after more than fifty years in 2001 Sela and Kharlampovich-Myasnikov answered it positively. Both works are voluminous and have not been absorbed yet. The techniques almost exclusively come from the disciplines mentioned above, hence it is no wonder that the question had to wait for their development. The great novelty of the methods and the depth of the needed results have made it hard to streamline any of the proofs. Despite the difficulties there is some considerable progress in the understanding of the first order theory of "the free group" and consequently first order theories of hyperbolic groups from the scopes of basic model theory, Shela's classification theory and geometric stability. In this talk I will survey what is known about these theories and what are the main open questions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123724&date=2019-02-22Student 3-Manifold Seminar, Feb 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124151&date=2019-02-22
This is a continuation of last week's talk about Stalling's work on ends of groups, with the Sphere Theorem as an application.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124151&date=2019-02-22