Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsAnalysis and PDE Seminar, Jan 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114370&date=2018-01-15
In this talk, we relate microlocal concentration of eigenfunctions to sup-norms and sub-manifold averages. In particular, we characterize the microlocal concentration of eigenfunctions with maximal sup-norm and average growth. We then exploit this characterization to derive geometric conditions under which maximal growth cannot occur. This talk is based on joint works with Yaiza Canzani and John Toth.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114370&date=2018-01-153-Manifold Seminar, Jan 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114443&date=2018-01-16
We'll discuss some topics that I hope to consider this semester, including a continuation of the discussion of computational complexity of 3-manifold invariants from last semester, and Kronheimer-Mrowka's work on instanton homology for webs, as well as anything of interest to participants in the seminar.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114443&date=2018-01-16Thematic Seminar: Number Theory, Jan 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114371&date=2018-01-16
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. We will discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity, as well as theorems about the distribution of non-abelian analogs of class groups of function fields that motivate this work.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114371&date=2018-01-16Probabilistic Operator Algebra Seminar, Jan 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114307&date=2018-01-17
Free infinitely divisible distributions (FID) distributions were introduced by Voiculescu. Recently many classically infinitely divisible distributions have been shown to be FID too, the first highly nontrivial one being the normal distribution found by Belinschi, Bozejko, Lehner and Speicher in 2011. Also several subclasses of FID distributions have been introduced and studied. I will try to summarize these results as well as open problems.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114307&date=2018-01-17Topology Seminar (Introductory Talk), Jan 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114450&date=2018-01-17
In this talk I will introduce the notion of a quasi-isometry and discuss the fundamental role it plays in geometric group theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114450&date=2018-01-17Number Theory Seminar, Jan 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114398&date=2018-01-17
This is joint work with Tasho Kaletha. The local Langlands correspondence predicts that representations of a reductive group G over a p-adic field are related to Galois representations into the Langlands dual of G. A conjecture of Kottwitz (as generalized by Rapoport and Viehmann) asserts that this relationship appears in a precise way in the cohomology of "local Shimura varieties", which were shown to exist by Scholze. We don't know how Galois acts on this cohomology yet, but we can verify much of the rest of the conjecture, in a large degree of generality, using a Lefschetz-Verdier fixed point formula.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114398&date=2018-01-17From stopping times to “spotting” times : a new framework for multiple testing, Jan 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114203&date=2018-01-17
Modern data science is often exploratory in nature, with hundreds or thousands of hypotheses being regularly tested on scientific datasets. The false discovery rate (FDR) has emerged as a dominant error metric in multiple hypothesis testing over the last two decades. I will argue that both (a) the FDR error metric, as well as (b) the current framework of multiple testing, where the scientist picks an arbitrary target error level (like 0.05) and the algorithm returns a set of rejected null hypotheses, may be rather inappropriate for exploratory data analysis.<br />
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I will show that, luckily, most existing FDR algorithms (BH, STAR, LORD, AdaPT, Knockoffs, and several others) naturally satisfy a more uniform notion of error, yielding simultaneous confidence bands for the false discovery proportion through the entire path of the algorithm. This makes it possible to flip the traditional roles of the algorithm and the scientist, allowing the scientist to make post-hoc decisions after seeing the realization of an algorithm on the data. For example, the scientist can instead achieve an error guarantee for all target error levels simultaneously (and hence for any data-dependent error level). Remarkably, there is a relatively small price for this added flexibility, the analogous guarantees being less than a factor of 2 looser than if the error level was prespecified. The theoretical basis for this advance is founded in the theory of martingales : we move from optional stopping (used in FDR proofs) to optional spotting by proving uniform concentration bounds on relevant exponential supermartingales. <br />
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This is joint work with Eugene Katsveich, but this talk will also cover some work with (alphabetically) Rina Barber, Jianbo Chen, Will Fithian, Kevin Jamieson, Michael Jordan, Lihua Lei, Max Rabinovich, Martin Wainwright, Fanny Yang and Tijana Zrnic.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114203&date=2018-01-17Applied Math Seminar, Jan 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114401&date=2018-01-17
In this talk, I advertise for a convex variational functional from statistical mechanics, which is particularly suitable for obtaining the free energy of high-dimensional order parameters from simulational sampling. In the numerical minimization of this variational functional, sampling difficulties related to ergodicity break-down are often alleviated. Two applications will be given. The first one is on Monte Carlo renormalization group simulations, where critical slowing down is eliminated in calculating the renormalized Hamiltonian and static critical exponents. The second one is on the nearest-neighbor 3D spin glass problem, where the Edward-Anderson overlap distribution can be obtained at temperatures much lower than the estimated spin glass transition temperature without the aid of parallel tempering. In these two examples, the optimization is fast and robust. Puzzles generated by this optimization process will also be discussed in the talk.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114401&date=2018-01-17Topology Seminar (Main Talk), Jan 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114451&date=2018-01-17
Boundaries of hyperbolic metric spaces have played an important role in the study of hyperbolic groups. We will discuss an analogous boundary for arbitrary finitely generated groups, called the Morse boundary, and present a recent theorem showing that in many cases, the Morse boundary determines the group up to quasi-isometry. (Joint work with M. Cordes and D. Murray)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114451&date=2018-01-17Seminar 217, Risk Management: Concrete examples of trend analyses and forward-looking modelling in Swiss Re's underwriting, Jan 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114313&date=2018-01-18
- In insurance, underwriting performance is a function of exposures, losses relative to exposures and premiums relative to exposures. Getting losses and loss trends right (--> cost of goods sold) is critically important. A small estimation mistake typically has a large impact on the bottom line.<br />
- Swiss Re is determining loss relevant trends using advanced analytics, often in collaboration with universities, government organizations, NGOs, rating agencies, consultants, investment management firms, lawyers, and others. Findings are used for both capital allocation and experience-based costing analyses.<br />
- In situations where the past is a poor predictor of the future, exposure-based rating analyses using forward-looking models are superior to the traditional experience-based approach. Swiss Re's proprietary forward-looking models are routinely used in costing.<br />
- The Swiss Re Institute professionalizes Swiss Re's R&D to improve its competitive advantage in risk selection and capital allocation in line with Swiss Re's strategic priorities.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114313&date=2018-01-18Thematic Seminar: Geometry, Jan 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114372&date=2018-01-18
Lattices in higher rank simple Lie groups are known to be extremely rigid. Examples of this are Margulis' superrigidity theorem, which shows they have very few linear represenations, and Margulis' arithmeticity theorem, which shows they are all constructed via number theory. Motivated by these and other results, in 1983 Zimmer made a number of conjectures about actions of these groups on compact manifolds. After providing some history and motivation, I will discuss a very recent result, proving many cases of the main conjecture. In this talk I will emphasize connections to homogeneous dynamics and particularly to issues of escape of mass that arise in the case of lattices which are not cocompact.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114372&date=2018-01-18Mathematics Department Colloquium, Jan 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114376&date=2018-01-19
According to Hilbert, the theory of complex multiplication, which brings together number theory and analysis, is not only the most beautiful part of mathematics but also of all science. "Complex multiplication" refers to a lattice in the complex numbers (or an elliptic curve) which admits endomorphisms by a ring larger than the integers. We will begin with Kronecker's "Jugendtraum" – the use of complex multiplication to solve Hilbert's twelfth problem. This will lead us into a discussion of Heegner points, and the solution of the Birch and Swinnerton-Dyer conjecture in certain cases. We will conclude with some recent work on the modular curve "at infinite level", and the unexpected role that complex multiplication plays in its geometry.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114376&date=2018-01-19Thematic Seminar: Probability Theory, Jan 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114373&date=2018-01-19
Models of random geometry have long been investigated in contexts such as the internet, fluid flow in porous media, and interface dynamics in statistical physics. To develop a refined understanding of such models, one often needs to study not only typical fluctuation theory but also the realm of atypical events. In this talk we describe such a program for two classical models of random geometry: percolation on the complete graph and random distortions of the Euclidean lattice. In particular, we will consider the large deviations behavior of the count of certain local structures in a sparse random network, and geodesics in a random metric space. The random geometry associated to typical instances of these rare events is an important topic of inquiry: this geometry can involve merely local structures, or more global ones. We will discuss some recent results concerning such phenomena, and connections to other areas of mathematics including random matrix theory, information theory, and algebraic and extremal combinatorics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114373&date=2018-01-19Combinatorics Seminar, Jan 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114453&date=2018-01-22
In 1944, Selberg evaluated a multivariate integral, which generalizes Euler's beta integral. In 1980, Askey conjectured a $q$-integral version of the the Selberg integral, which was proved independently by Habsieger and Kadell in 1988. In this talk, we focus on the combinatorial aspects of the Selberg integral. First, we review the following fact observed by Igor Pak: evaluating the Selberg integral is essentially the same as counting the linear extensions of a certain poset. Considering $q$-integrals over order polytopes, we give a combinatorial interpretation for Askey's $q$-Selberg integral. We also find a connection between the Selberg integral and Young tableaux. As applications we enumerate Young tableaux of various shapes.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114453&date=2018-01-22Probabilistic Operator Algebra Seminar, Jan 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114444&date=2018-01-22
With the introduction of free independence by D.V. Voiculescu, it became clear that in the framework of non-commutative probability there are other notions of independence different than that of (classical) independence. In 1997, R. Speicher defined a notion of universal product for which he showed that there are three types of independence. In the category of unital algebras the tensor and free independence are the only existing ones. On the other hand when algebras are not required to have a unit, the product provided by Boolean independence is also admitted as a universal product. The Boolean convolution between measures was formally introduced by Speicher and R. Woroudi in 1993, although it had previously appeared in the literature in different contexts, for example, as partial cumulants in stochastic differential equations. Later, in 2006, H. Bercovici provided the product for Hilbert spaces that, in the context of operator algebras, corresponds to the Boolean convolution between measures. In this talk we will survey the basics of Boolean probability together with some results that show the similarities and differences that it has with the classical theory of probability.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114444&date=2018-01-22Differential Geometry Seminar, Jan 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114399&date=2018-01-22
We establish a comparison theorem for polyhedra in 3-manifolds with nonnegative scalar curvature, answering affirmatively a dihedral rigidity conjecture by Gromov. For a large collection of polyhedra with interior non-negative scalar curvature and mean convex faces, we prove that the dihedral angles along its edges cannot be everywhere less or equal than those of the corresponding Euclidean model, unless it is a isometric to a flat polyhedron.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114399&date=2018-01-22Arithmetic Geometry and Number Theory RTG Seminar, Jan 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114780&date=2018-01-22
We will discuss recent developments in the computation of Brauer groups of some algebraic stacks, namely the moduli stack of elliptic curves $\mathscr M_{1,1}$ and torsion $\mathbb G_m$-gerbes.<br />
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Seminar Format: The seminar consists of two 50-minute talks, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00), with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114780&date=2018-01-22Understanding rare events in models of statistical mechanics, Jan 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114509&date=2018-01-22
Statistical mechanics models are ubiquitous at the interface of probability theory, information<br />
theory, and inference problems in high dimensions. In this talk, we will focus on<br />
sparse networks, and polymer models on lattices. The study of rare behavior (large deviations)<br />
is intimately related to the understanding of such models. In particular, we will<br />
consider the rare events that a sparse random network has an atypical number of certain<br />
local structures and that a polymer in random media has atypical weight. Such events can<br />
have different geometric consequences, ranging from local to more global. We will discuss<br />
some recent results concerning such phenomena, and connections to stochastic block models,<br />
exponential random graphs, eigenvalues of random matrices, and fundamental growth<br />
models.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114509&date=2018-01-22Thematic Seminar: Numerical Methods, Jan 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114374&date=2018-01-22
Machine intelligence for processing big data sets is big business. A mathematician's point of view has led to (1) effective large-scale principal component analysis and singular value decomposition, and (2) theoretical foundations for convolutional networks (convolutional networks underpin the recent revolution in artificial intelligence).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114374&date=2018-01-22Understanding rare events in models of statistical mechanics, Jan 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114559&date=2018-01-22
Statistical mechanics models are ubiquitous at the interface of probability theory, information<br />
theory, and inference problems in high dimensions. In this talk, we will focus on<br />
sparse networks, and polymer models on lattices. The study of rare behavior (large deviations)<br />
is intimately related to the understanding of such models. In particular, we will<br />
consider the rare events that a sparse random network has an atypical number of certain<br />
local structures and that a polymer in random media has atypical weight. Such events can<br />
have different geometric consequences, ranging from local to more global. We will discuss<br />
some recent results concerning such phenomena, and connections to stochastic block models,<br />
exponential random graphs, eigenvalues of random matrices, and fundamental growth<br />
models.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114559&date=2018-01-223-Manifold Seminar, Jan 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114774&date=2018-01-23
We'll discuss a proof that knot recognition is in NP, using a certificate that encodes a sutured manifold hierarchy.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114774&date=2018-01-23Thematic Seminar: Applied Mathematics, Jan 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114402&date=2018-01-23
Fiber-reinforced structures arise in many engineering and biological applications. Examples include space inflatable habitats, vascular stents supporting compliant vascular walls, and aortic valve leaflets. In all these examples a metallic mesh, or a collection of fibers, is used to support an elastic structure, and the resulting composite structure has novel mechanical characteristics preferred over the characteristics of each individual component. These structures interact with the surrounding deformable medium, e.g., blood flow or air flow, or another elastic structure, constituting a fluid-structure interaction (FSI) problem. Modeling and computer simulation of this class of FSI problems is important for manufacturing and design of novel materials, space habitats, and novel medical constructs.<br />
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Mathematically, these problems give rise to a class of highly nonlinear, moving-boundary problems for systems of partial differential equations of mixed type. To date, there is no general existence theory for solutions of this class of problems, and numerical methodology relies mostly on monolithic/implicit schemes, which suffer from bad condition numbers associated with the fluid and structure sub-problems.<br />
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In this talk we present a unified mathematical framework to study existence of weak solutions to FSI problems involving incompressible, viscous fluids and elastic structures. The mathematical framework provides a constructive existence proof, and a partitioned, loosely coupled scheme for the numerical solution of this class of FSI problems. The constructive existence proof is based on time-discretization via operator splitting, and on our recent extension of the Aubin-Lions-Simon compactness lemma to problems on moving domains. The resulting numerical scheme has been applied to problems in cardiovascular medicine, showing excellent performance, and providing medically beneficial information.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114402&date=2018-01-23Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Jan 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114773&date=2018-01-23
The two topics for the student portion this semester are Intersection Theory and Linkage. A detailed outline of the topics for the first half of the seminar can be found at "math.berkeley.edu/~ritvik/Eisenbud-Seminar-Outline.pdf". In the meeting we will describe the main goals of this seminar and sign-up speakers for respective topics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114773&date=2018-01-23Topology Seminar (Introductory Talk), Jan 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114728&date=2018-01-24
We will introduce Thurston's norm on the second homology of a 3-manifold, and some associated constructions including branched surfaces and Agol’s veering triangulation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114728&date=2018-01-24Topology Seminar (Main Talk), Jan 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114727&date=2018-01-24
Let \(M\) be a closed hyperbolic 3-manifold with a fibered face \(\sigma\) of the unit ball of the Thurston norm on \(H_2(M)\). If \(M\) satisfies a certain condition related to Agol’s veering triangulation, we can construct a taut branched surface in \(M\) spanning \(\sigma\). This partially answers a 1986 question of Oertel, and extends an earlier partial answer due to Mosher.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114727&date=2018-01-24Applied Math Seminar, Jan 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114775&date=2018-01-24
(Note the special location) A spacetime simulation region can be subdivided into tent-shaped subregions. Tents appear to be natural for solving hyperbolic equations. Indeed, one can ensure causality by constraining the height of the tent pole. More precisely, the domain of dependence of all points within the tent can be guaranteed to be contained within the tent, by constraining the tent pole height. We consider techniques to advance the numerical solution of a hyperbolic problem by progressively meshing a spacetime domain by tent shaped objects. Such tent pitching schemes have the ability to naturally advance in time by different amounts at different spatial locations. One obtains spacetime discontinuous Galerkin (SDG) schemes - extensively studied by many authors - when the hyperbolic system on the tent is discretized in spacetime. We pursue another alternative by mapping each tent to a spacetime cylinder. These maps transform tents into domains where space and time are separated, thus allowing standard methods to be used within tents. Several open mathematical and computational issues surrounding these methods will be touched upon.<br />
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Reference: J. Gopalakrishnan, J. Schlberl, and C. Wintersteiger. "Mapped tent pitching schemes for hyperbolic systems." SIAM J Sci Comp, 39:6, p.B1043-B1063, 2017.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114775&date=2018-01-24Thematic Seminar: Partial Differential Equations, Jan 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114375&date=2018-01-24
An intriguing feature of the explicit charged (Reissner-Nordstrom) or spinning (Kerr) black hole spacetimes is the existence of a regular Cauchy horizon, beyond which the Einstein equation loses its predictive power. The strong cosmic censorship conjecture of Penrose is a bold claim that, nevertheless, such a pathological behavior is nongeneric.<br />
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In this lecture, I will give a short introduction to general relativity and the strong cosmic censorship conjecture. Then I will describe my recent joint work with J. Luk, where we rigorously establish a version of this conjecture for the Einstein-Maxwell-(real)-scalar-field system in spherical symmetry, which has long been studied by physicists and mathematicians as a useful model for this problem.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114375&date=2018-01-24Workshop: Introduction to Deep Learning, Jan 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114699&date=2018-01-24
Are you interested in learning what's the machinery behind the Deep Learning hype? Come to ML@B's Intro to Deep Learning Workshop! <br />
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We will teach you how neural networks work and how to use them through hands-on demos. The workshop is structured so that you have enough knowledge to get the most out of our future workshops. <br />
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You can find the full list at ml.berkeley.edu/workshops. Although no strict prerequisites, Python knowledge and knowledge of multivariable calculus will be helpful.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114699&date=2018-01-24Paris/Berkeley/Bonn/Zürich Analysis Seminar, Jan 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114308&date=2018-01-25
I show that on a compact hyperbolic surface, the mass of an $L^2$-normalized eigenfunction of the Laplacian on any nonempty open set is bounded below by a positive constant depending on the set, but not on the eigenvalue. This statement, more precisely its stronger semiclassical version, has many applications including control for the Schrödinger equation and the full support property for semiclassical defect measures. The key new ingredient of the proof is a fractal uncertainty principle, stating that no function can be localized close to a porous set in both position and frequency. This talk is based on joint works with Long Jin and with Jean Bourgain.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114308&date=2018-01-25Seminar 217, Risk Management: PageRank on directed complex networks, Jan 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114314&date=2018-01-25
The talk will center around a set of recent results on the analysis of Google’s PageRank algorithm on directed complex networks. In particular, it will focus on the so-called power-law hypothesis, which states that the distribution of the ranks produced by PageRank on a scale-free graph (whose in-degree distribution follows a power-law) also follows a power-law with the same tail-index as the in-degree. We show that the distribution of PageRank on both the directed configuration model and the inhomogeneous random digraph does indeed follow a power-law whenever the in-degree does, and we provide explicit asymptotic limits for it. Moreover, our asymptotic expressions exhibit qualitatively different behaviors depending on the level of dependence between the in-degree and out-degree of each vertex. On graphs where the in-degree and out-degree are close to independent, our main theorem predicts that PageRank will tend to grant high ranks to vertices with large in-degrees, but also to vertices who have highly-ranked inbound neighbors. However, when the in-degree and out-degree are positively correlated, the latter can potentially disappear, strengthening the impact of high-degree vertices on the ranks produced by the algorithm.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114314&date=2018-01-25DiPerna Lecture, Jan 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114730&date=2018-01-25
We will give an overview of some of the developments in recent years dealing with the description of asymptotic states of solutions to semilinear evolution equations ("soliton resolution conjecture"). New results will be presented on damped subcritical Klein-Gordon equations, joint with Nicolas Burq and Genevieve Raugel.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114730&date=2018-01-25Student Probability/PDE Seminar, Jan 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114829&date=2018-01-26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114829&date=2018-01-26Applied Math Seminar, Jan 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114776&date=2018-01-26
(Note special date and location) A wide variety of physical and biological systems can be described as continuum limits of interacting particles. Many of these problems are gradient flows and their dynamics are governed by a monotonically decreasing interaction energy that is often non-local in nature. We show how to exploit these energies numerically, analytically, and asymptotically to characterize the observed behavior. We describe three such systems. In the first, a Langmuir layer, line tension (the two-dimensional analog of surface tension) drives the fluid domains to become circular and the rate of relaxation to these circular domains can be used to deduce the magnitude of the line tension forces. In the second, a Hele-Shaw problem, vexing changes in topology are observed. The third system models the formation of the convoluted fingered domains observed experimentally in ferrofluids for which pattern formation is driven by line tension and dipole-dipole repulsion. We show that noise in this system plays an unexpected but essential role and deduce an algorithm for extracting the dipole strength using only a shape's perimeter and morphology.<br />
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Biosketch: Andrew Bernoff is the Kenneth & Diana Jonsson Professor of Mathematics at Harvey Mudd College. His research specializes in bridging the gaps between Mathematics, Physics, Biology and Engineering with a particular emphasis on using dynamical systems methods to understand experiments and natural phenomena. Prof. Bernoff was an undergraduate at MIT where he received BS degrees in Mathematics and Physics. He was awarded a Marshall Scholarship to pursue a PhD at the University of Cambridge in England. His PhD studies were on the application of dynamical systems methods in fluid mechanics in the Department of Applied Mathematics and Theoretical Physics (DAMTP). Prof. Bernoff spent time on the faculty at Northwestern before settling in at Harvey Mudd College. He is passionate about mentoring undergraduate research, coaching the Harvey Mudd College Putnam Team, and supporting Harvey Mudd College’s Clinic Program, a year-long practicum in which teams of undergraduates work for industrial sponsors on real-world problems and applications. His research program centers on understanding the behavior of fluids at small scales and modeling the swarming of organisms, in particular locusts.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114776&date=2018-01-26Combinatorics Seminar, Jan 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114454&date=2018-01-29
We introduce and study a new class of permutations which arises from the automorphisms of the Cuntz algebra. I will define this class, explain its relation to the Cuntz algebra, present results about symmetries, constructions, characterizations, and enumeration of these permutations, and discuss some open problems and conjectures. This is joint work with Roberto Conti.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114454&date=2018-01-29Probabilistic Operator Algebra Seminar, Jan 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114830&date=2018-01-29
Monotone independence is another notion of independence in non-commutative probability theory which differs from classical, free and Boolean independences. In this talk I will derive a basic formula for monotone convolution of probability measures where the reciprocal Cauchy transform plays a role similar to the one played by the Fourier transform in classical probability.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114830&date=2018-01-29Differential Geometry Seminar, Jan 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114400&date=2018-01-29
One of main purposes in the convergence theory (with uniform Ricci bounds from below) is to find geometric/analytic quantities which are continuous with respect to measured Gromov-Hausdorff convergence. The diameter is a trivial geometric example. On the other hand the \(k^{th}\) eigenvalue of the Laplacian is a nontrivial analytic example for all \(k\), which was proven by Cheeger-Colding. In this talk we provide a new nontrivial geometric example, so-called Cheeger's isoperimetric constant. In the proof, BV-functions and \(L^1\)-Bakry-Emery estimate play key roles. Moreover we give a deep relationship between these three continuous quantities via PDEs. This is a joint work with L. Ambrosio.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114400&date=2018-01-29Arithmetic Geometry and Number Theory RTG Seminar, Jan 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114781&date=2018-01-29
Let $X$ be an algebraic variety over a field $k$. Which representations of $\pi _1(X)$ arise from geometry, e.g. as monodromy representations on the cohomology of a family of varieties over $X$? We study this question by analyzing the action of the Galois group of $k$ on the fundamental group of $X$, and prove several fundamental structural results about this action.<br />
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As a sample application of our techniques, I show that if $X$ is a normal variety over a field of characteristic zero, and $p$ is a prime, then there exists an integer $N=N(X,p)$ such that any non-trivial $p$-adic representation of the fundamental group of $X$, which arises from geometry, is non-trivial mod $p^N$.<br />
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Seminar Format: The seminar consists of two 50-minute talks, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00), with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114781&date=2018-01-29Analysis and PDE Seminar, Jan 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114729&date=2018-01-29
For a finite measure \(\mu \) on the real line, its Fourier dimension is defined using the rate of polynomial decay of the Fourier transform \(\hat \mu \). The Fourier dimension of \(\mu \) may be much smaller than the Hausdorff dimension of the support of \(\mu \): a classical example is the Cantor measure on the mid-third Cantor set which has Fourier dimension equal to 0.<br />
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I will present a joint result with J. Bourgain showing that the Patterson-Sullivan measure on the limit set of a convex co-compact group of fractional linear transformations has positive Fourier dimension. The proof uses advanced tools from additive combinatorics (the discretized sum-product theorem) and exploits the fact that fractional linear transformations are (generally) not linear. An application is a new spectral gap result for convex co-compact hyperbolic surfaces.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114729&date=2018-01-29Provably Secure Machine Learning, Jan 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114795&date=2018-01-29
Deployed machine learning systems create a new class of computer security vulnerabilities <br />
where, rather than attacking the integrity of the software itself, malicious actors exploit the <br />
statistical nature of the learning algorithms. For instance, attackers can add fake training data, <br />
or strategically manipulate input covariates at test time.<br />
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Attempts so far to defend against these attacks have focused on empirical performance against <br />
known sets of attacks. I will argue that this is a fundamentally inadequate paradigm for achieving <br />
meaningful security guarantees, and that we instead need algorithms that are provably secure by <br />
design, by being robust to worst-case perturbations of the train or test data. This will require <br />
revisiting classical problems in robust optimization and statistics with an eye towards the security <br />
requirements of modern machine learning systems. In particular, we will develop new theory for <br />
robust statistics in high-dimensional settings, and for robust optimization of non-convex models.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114795&date=2018-01-29Differential Geometry Seminar, Jan 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114828&date=2018-01-30
Ricci flow theory has been developing rapidly over the last couple of years, with the ability to handle Ricci flows with unbounded curvature finally becoming a reality. This is vastly expanding the range of potential applications. I will describe some recent work in this direction with Miles Simon that shows the right way to pose the 3D Ricci flow in this setting in order to obtain applications. Amongst these applications is a proof that 3D Ricci limit spaces are locally bi-Holder homeomorphic to smooth manifolds, which solves more than an old conjecture of Anderson-Cheeger-Colding-Tian in this dimension.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114828&date=2018-01-30Statistical Inference for Finite Alphabet Structures, Jan 31
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114404&date=2018-01-31
A challenging problem in cancer genetics is that tumors often consist of a few different groups of cells, so called clones, where each clone has different mutations, like copy-number (CN) variations. In whole genome sequencing the mutations of the different clones get mixed up, according to their relative unknown proportion in the tumor. However, CN's of single clones can only take values in a known finite set, denoted as the alphabet.<br />
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In this talk, we show how this structural information can solve the problem, which corresponds to blind source separation with finite alphabets.<br />
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First, we give a complete combinatorial characterization of identifiability, which lays the fundamentals of exact recovery theory in a completely new sparsity framework (Behr and Munk, 2017, IEEE Trans. Inf. Theory). In a statistical change-point regression model, as it appears, e.g., in CN applications, we introduce a multiscale approach and derive estimators with optimal convergence rates (up to log-factors) and uniform confidence statements for all quantities, including statistical error guarantees for the minimal “model dimension”, a task which is in general difficult to obtain (Behr et al., 2017, Ann. Stat., to appear). The estimator is computed efficiently using dynamic programming.<br />
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Finally, we give minimax results for the multivariate case, as it appears, for instance, in wireless digital communications. We outline how the combinatorial structure of finite alphabets arise challenging questions in computational statistics, such as potential optimality gaps.<br />
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This is joint work with Prof. Axel Munk (University of Göttingen) and Prof. Chris Holmes (Wellcome Trust Centre for Human Genetics, University of Oxford).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114404&date=2018-01-31Applied Math Seminar, Jan 31
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114777&date=2018-01-31
Implicit time integration for discontinuous Galerkin (DG) discretizations is important in the context of boundary layer flows, anisotropic, unstructured meshes, and high degree polynomial approximations. Effective preconditioning strategies are essential to the efficient iterative solution of the resulting large, sparse linear systems. In this talk, I will discuss two topics: (1) fully implicit Runge-Kutta solvers, and (2) tensor-product preconditioners for very high polynomial degrees.<br />
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(1) There are several advantages to using fully-coupled implicit Runge-Kutta schemes compared with traditional DIRK or BDF methods. However, such methods couple all of the Runge-Kutta stages, resulting in a much larger system of equations. We transform the resulting system of equations to maximize sparsity, and then develop several ILU-based preconditioners with favorable performance properties. These solvers have the additional advantage that they allow for parallelism across the stages.<br />
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(2) Furthermore, the DG method allows for arbitrary order of accuracy, according to the degree of polynomial approximation used. High-degree polynomials result in extremely restrictive CFL conditions, motivating the use of implicit solvers. We develop efficient solvers and preconditioners that exploit the natural tensor-product structure of quadrilateral and hexahedral grids in order to obtain methods with optimal computational complexity.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114777&date=2018-01-31