Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsNorthern California Symplectic Geometry Seminar, Dec 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121842&date=2018-12-03
We explain how using the Floer version of persistence homology, we can find invariants of Rokhlin equivalence classes i.e. $f \simeq g$ if there is a chain $f_0=f,.... f_n=g$ such that the $C^0$ closure of the conjugacy orbit of $f_i$ and $f_{i+1}$ meet. We shall explain the $2$ dimensional case, and its generalization to higher dimensions using the $C^0$ continuity of γ explained in Sobhan's talk.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121842&date=2018-12-03Arithmetic Geometry and Number Theory RTG Seminar, Dec 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121844&date=2018-12-03
Let $A$ denote a non-constant ordinary abelian surface over a global function field (of characteristic p > 2) with good reduction everywhere. Suppose that $A$ does not have real multiplication by any real quadratic field with discriminant a multiple of $p$. Then we prove that there are infinitely many places modulo which $A$ is isogenous to the product of two elliptic curves. This is joint work with Davesh Maulik and Yunqing Tang.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121844&date=2018-12-03Northern California Symplectic Geometry Seminar, Dec 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121843&date=2018-12-03
We will show that the spectral norm on the group of Hamiltonian diffeomorphisms, introduced in the works of Viterbo, Schwarz and Oh, is continuous with respect to the $C^0$ topology, when M is symplectically aspherical. This statement was previously proven only in the case of closed surfaces. This has numerous applications one of which is a generalization of the Arnold conjecture for Hamiltonian homeomorphisms.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121843&date=2018-12-03Analysis and PDE Seminar, Dec 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121729&date=2018-12-03
The focus of this talk will be on nonlinear moving-boundary problems involving incompressible, viscous fluids and elastic structures. The fluid and structure are coupled via two sets of coupling conditions, which are imposed on a deformed fluid-structure interface. The main difficulty in studying this class of problems stems from the strong geometric nonlinearity due to the nonlinear fluid-structure coupling. We have recently developed a robust framework for proving existence of weak solutions to this class of problems, allowing the treatment of various structures (Koiter shell, multi-layered composite structures, mesh-supported structures), and various coupling conditions (no-slip and Navier slip). The existence proofs are constructive: they are based on Rothe’s method (semi- discretization in time), and on our generalization of the Lions-Aubin-Simon’s compactness lemma to moving boundary problems. Applications of this strategy to the simulations of real-life problems will be shown. A new problem involving a design of bioartificial pancreas (together with Dr. Roy of UCSD Bioengineering) will be discussed.<br />
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This is a joint work with B. Muha, University of Zagreb in Croatia.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121729&date=2018-12-03Symplectic Working Group, Dec 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121895&date=2018-12-04
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121895&date=2018-12-04Student Harmonic Analysis and PDE Seminar (HADES), Dec 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121907&date=2018-12-04
We consider the local well-posedness of the Cauchy problem for the gravity water waves equations, which model the free interface between a fluid and air in the presence of gravity. It has been known that by using dispersive effects, one can lower the regularity threshold for well-posedness below that which is attainable by energy estimates alone. Using a paradifferential reduction of Alazard-Burq-Zuily and low regularity Strichartz estimates, we apply this idea to the well-posedness of the gravity water waves equations in arbitrary space dimension. Further, in two space dimensions, we discuss how one can apply local smoothing effects to further extend this result.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121907&date=2018-12-04Maps of a rising water table: The hidden component of sea level rise, Dec 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120058&date=2018-12-04
Map-based data viewers have been available for several years that reveal where coastal flooding is likely to occur as oceans warm and ice sheets melt. Recently, geologists have begun to study the influence of sea level rise on groundwater, and have concluded that in some coastal areas, as much or more land could flood as a result of rising groundwater than will flood directly from saltwater. Yet almost no coastal areas have maps available of depth to the water table, below which soils are saturated with water. My students and I have recently made a map of depth to the water table around San Francisco Bay, and this map reveals previously unrecognized vulnerabilities to sea level rise. By taking groundwater into account, we have revealed some potential problems with adaptation that relies on seawalls and levees alone, and developed an alternative strategy for urban areas that might allow us to live with higher water. This talk will present both the new maps of coastal groundwater depth and some strategies for urban adaptation.<br />
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The Berkeley Distinguished Lectures in Data Science, co-hosted by the Berkeley Institute for Data Science (BIDS) and the Berkeley Division of Data Sciences, features Berkeley faculty doing visionary research that illustrates the character of the ongoing data revolution. This lecture series is offered to engage our diverse campus community and enrich active connections among colleagues. All campus community members are welcome and encouraged to attend. Arrive at 3:30 PM for light refreshments and discussion prior to the formal presentation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120058&date=2018-12-04Tails of the KPZ equation, Dec 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121894&date=2018-12-05
The KPZ equation is a fundamental stochastic PDE related to modeling random growth processes, Burgers turbulence, interacting particle system, random polymers etc. In this talk, we focus on the tail probabilities of the solution of the KPZ equation. For instance, we investigate the probability of the solution being smaller or larger than the expected value. Our analysis is based on an exact identity between the KPZ equation and the Airy point process (which arises at the edge of the spectrum of the random Hermitian matrices) and the Brownian Gibbs property of the KPZ line ensemble.<br />
This talk will be based on a joint work with my advisor Prof. Ivan Corwin.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121894&date=2018-12-05Representation Theory and Mathematical Physics Seminar, Dec 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121644&date=2018-12-05
The pentagram map was introduced by Richard Schwartz in 1992, and is now one of the most renowned discrete integrable systems which has deep connections with such topics as cluster algebras, dimer models etc. In this talk I will present a geometric construction which identifies the pentagram map, as well as its various multidimensional generalisations, with refactorization type mappings in Poisson-Lie groups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121644&date=2018-12-05Center for Computational Biology Seminar, Dec 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120943&date=2018-12-05
Full-length alternative transcript isoform analysis with nanopore sequencing<br />
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Abstract: <br />
Our group aims to understand the mechanisms of alternative RNA splicing regulation and splicing dysregulation in cancer. Short-read, high-throughput cDNA sequencing (RNA-Seq) has revolutionized our ability to profile RNA splicing; however, this approach cannot capture the full complexity of RNA transcripts. First, “RNA-Seq” should, more appropriately, be called cDNA-Seq—it is not sequencing RNA directly. Second, short-reads limit our ability to accurately identify and quantify full-length RNA isoforms. For a more comprehensive characterization of alternative transcript isoform expression, we have been developing computational approaches to analyze long-read nanopore sequencing data. I will present a study to identify differentially expressed isoforms from nanopore cDNA sequencing of isogenic cell lines with and without a mutation in U2AF1, which is a recurrently mutated splicing factor in cancer. I will also present our analysis of native RNA sequencing of the GM12878 cell line, as part of the Nanopore RNA Consortium. Utilizing the full benefit of directly sequencing full-length RNA transcripts, we identified alternative transcript isoforms and their association with allele expression, RNA modifications, and poly(A) tail length. <br />
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Bio: <br />
Angela Brooks is an Assistant Professor of Biomolecular Engineering at UC Santa Cruz. She received her Ph.D. in Molecular and Cell Biology with a Designated Emphasis in Computational and Genomic Biology from UC Berkeley with Steven Brenner. She was a post-doctoral fellow at the Dana-Farber Cancer Institute and the Broad Institute with Matthew Meyerson.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120943&date=2018-12-05Applied Math Seminar, Dec 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121521&date=2018-12-06
Filters in a Convolutional Neural Network (CNN) contain model parameters learned from data. The properties of convolutional filters in a trained deep network directly affect the quality of the feature representation being learned. In this talk, we introduce a framework for decomposing convolutional filters over a truncated expansion under pre-fixed bases, where the expansion coefficients are adaptive. Such a structure not only reduces the number of trainable parameters and computational load but also imposes filter regularity by bases truncation. Apart from maintaining prediction accuracy across image classification datasets, the decomposed-filter CNN also produces a stable representation with respect to input variations proved under generic assumptions. The framework extends to group-equivariant CNNs where it significantly reduces the model complexity and demonstrates improved stability of the trained network. Joint work with Qiang Qiu, Robert Calderbank, and Guillermo Sapiro.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121521&date=2018-12-06Representation Theory and Mathematical Physics Seminar, Dec 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121927&date=2018-12-06
Virtual knot theory is a generalization of classical knot theory that studies stabilized knots and links in thickened surfaces. Two knots (links) in thickened surfaces are said to be stably equivalent if they can be obtained one from another by a finite sequence of ambient isotopies along with surgeries on their complements (that can change of genus of the embedding surface). There is a diagrammatic theory that captures stable equivalence. One adds virtual crossings (neither over nor under) and rules for handling them that generalize the Reidemeister moves. Then virtual knots can be studied using strictly planar diagrams. This means that one has access to both a rich background of combinatorial topology and the three dimensional topology of the thickened surfaces. This talk will discuss the basic definitions for virtual knot theory and the construction of a number of invariants of interest, including the Jones polynomial, the arrow polynomial and the affine index polynomial, Khovanov homology and relations with virtual knot cobordism. We will discuss how quantum link invariants extend to virtual knot theory and we will attempt to discuss how virtual knot theory could or should be related to physics and quantum information theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121927&date=2018-12-06Representation Theory and Mathematical Physics Seminar, Dec 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121956&date=2018-12-06
We will discuss the Arkhipov's twisting functor associated to a positive root of a complex simple finite-dimensional Lie algebra. By applying this twisting functor for a non-simple root on generalized Verma modules we obtain the so called partial Gelfand-Tsetlin modules, which are weight modules outside the category \(\mathcal O\). The talk is based on joint results with Vyacheslav Futorny and Luis Enrique Ramirez.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121956&date=2018-12-06Analysis and PDE Seminar, Dec 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122019&date=2018-12-10
From Helmholtz to vaping hipsters, the dynamics of vortex filaments, i.e. fluids with vorticity concentrated along a smooth curve, has been a topic of significant interest in fluid dynamics. The global well-posedness of vortex filaments with small circulation follows from the theory of mild solutions of the 3d Navier-Stokes equations at critical regularity. However, for filaments with large circulation these results no longer apply. In this talk we discuss a proof of well-posedness (in a suitable sense) for vortex filaments of arbitrary circulation. Besides their physical interest, these results are the first to give well-posedness in a neighborhood of large self-similar solutions of the 3d Navier-Stokes without additional symmetry assumptions. This is joint work with Jacob Bedrossian and Pierre Germain.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122019&date=2018-12-10