Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsR bootcamp, Aug 19-20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=109510&date=2017-08-20
The Statistics Department and D-Lab are offering an<br />
introductory short course on the statistical/data science<br />
software R on Saturday-Sunday, August 19-20. The short<br />
course will be a thorough introduction to working with<br />
data, statistical analysis, and programming in R,<br />
with no prior knowledge assumed. Please see<br />
http://dlab.berkeley.edu/training/r-bootcamp-2017 for<br />
more details. Attendance is free of charge.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=109510&date=2017-08-20Berkeley-Tokyo Summer School "Geometry, Representation Theory, and Mathematical Physics", Aug 21
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110510&date=2017-08-21
In my talk I will overview new classes of integrable systems associated with Nakajima quiver varieties. I will explain the geometric construction of quantum Rmatrices, commuting families of Hamiltonians and corresponding Bethe equations. I will discuss relations of these systems with quantum cohomology and quantum K-theory of Nakajima varieties.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110510&date=2017-08-21Probabilistic Operator Algebra Seminar, Aug 21
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110629&date=2017-08-21
Given an n-tuple of non-commutative random variables, its free Stein discrepancy relative to the semicircle law measures how close the distribution is to the semicircle law. By considering free Stein discrepancies relative to a broader class of laws, one can define a quantity called the free Stein information. In this talk, we will discuss this and its relation to other free probabilistic quantities such as the free Fisher information and the non-microstates free entropy dimension.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110629&date=2017-08-21Berkeley-Tokyo Summer School "Geometry, Representation Theory, and Mathematical Physics", Aug 21
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110511&date=2017-08-21
In these talks we will describe an approach to branching laws for highest weight integrable representations of affine Lie algebras based on fusion product and modular tensor categories. Our main emphasis will be on branching laws related with level rank dualityhttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110511&date=2017-08-21Berkeley-Tokyo Summer School "Geometry, Representation Theory, and Mathematical Physics", Aug 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110836&date=2017-08-22
In these talks we will describe an approach to branching laws for highest weight integrable representations of affine Lie algebras based on fusion product and modular tensor categories. Our main emphasis will be on branching laws related with level rank dualityhttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110836&date=2017-08-22Berkeley-Tokyo Summer School "Geometry, Representation Theory, and Mathematical Physics", Aug 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110837&date=2017-08-22
A dimer model is a bicolored graph on a real 2-torus encoding the information of a quiver with potential. It originates from statistical mechanics, and is related to various branches of mathematics. In the talk, we will give an introduction to the theory of dimer models and its application to homological mirror symmetry.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110837&date=2017-08-22Berkeley-Tokyo Summer School "Geometry, Representation Theory, and Mathematical Physics", Aug 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110838&date=2017-08-22
A dimer model is a bicolored graph on a real 2-torus encoding the information of a quiver with potential. It originates from statistical mechanics, and is related to various branches of mathematics. In the talk, we will give an introduction to the theory of dimer models and its application to homological mirror symmetry.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110838&date=2017-08-22Phase Transitions in Activated Random Walk, Aug 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110551&date=2017-08-23
On a locally finite graph, consider the following interacting particle system, known as<br />
Activated Random Walk (ARW). Start with a mass density µ of initially active particles, each of<br />
which performs a continuous time nearest neighbour symmetric random walk at rate one and falls<br />
asleep at rate λ > 0. Sleepy particles become active on coming in contact with active particles.<br />
I shall describe two recent works on this model: one on the infinite lattice Z, the second on the<br />
finite periodic lattice Z /n Z. On Z, Rolla and Sidoravicius (Invent. Math., 2012) recently showed<br />
that for small enough particle density, almost surely the number of jumps at each site is finite. We<br />
complement the Rolla-Sidoravicius result by confirming a further physics prediction establishing<br />
that the critical density goes to zero along with the sleep rate. On the n-cycle, if the total number<br />
of particles is no more than n, almost surely the process reaches an absorbing state. We show a<br />
parallel quantitative phase transition by showing that the total number of jumps until absorption<br />
scales linearly in n if µ < λ/(λ+1) and exponentially in n if λ is sufficiently small compared to µ.<br />
Based on joint works with Shirshendu Ganguly, Christopher Hoffman, Jacob Richey.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110551&date=2017-08-23Introduction to LaTeX using Collaboration Tools, Aug 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110268&date=2017-08-24
This workshop is an introduction to the LaTeX typesetting language. Document structure, templates, and commonly used syntax will be introduced and practiced during this hands-on workshop. Additionally, attendees will learn about the benefits of Overleaf and ShareLaTeX, two online LaTeX collaboration tools that the Library is piloting. This is a hands-on workshop - please bring a laptop (the library can provide one if you don’t have a laptop).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110268&date=2017-08-24Neyman Seminar: Patrick Wolfe, Aug 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110614&date=2017-08-24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110614&date=2017-08-24Mathematics Department Colloquium, Aug 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110345&date=2017-08-24
We look at sets of integer points in the plane, and discuss possible definitions of when such a set is "complicated"—this might be the case if it is not the set of integer solutions to some system of polynomial equations and inequalities. Let’s together work out lots of examples, and on the way let’s try to develop criteria and proof techniques$\ldots$.<br />
<br />
The examples that motivated our study come from polytope theory: Many question of the type "What are the possible pairs of (number of vertices, number of edges) for 5-dimensional polytopes?'' have been asked, many of them with simple and complete answers, but in other cases the answer looks complicated. Our main result says: In some cases it IS complicated! (Joint work with Hannah Sj\"oberg.)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110345&date=2017-08-24Logic Colloquium, Aug 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110512&date=2017-08-25
In 1925, Tarski posed the problem of whether a disc in $R^2$ can be partitioned into finitely many pieces which can be rearranged by isometries to form a square of the same area. Unlike the Banach-Tarski paradox in $R^3$, it can be shown that two Lebesgue measurable sets in $R^2$ cannot be equidecomposed by isometries unless they have the same measure. Hence, the disk and square must necessarily be of the same area.<br />
<br />
In 1990, Laczkovich showed that Tarski's circle squaring problem has a positive answer using the axiom of choice. We give a completely constructive solution to the problem and describe an explicit (Borel) way to equidecompose a circle and a square. This answers a question of Wagon.<br />
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Our proof has three main ingredients. The first is work of Laczkovich in Diophantine approximation. The second is recent progress in a research program in descriptive set theory to understand how the complexity of a countable group is related to the Borel cardinality of the equivalence relations generated by its Borel actions. The third ingredient is ideas coming from the study of flows in networks.<br />
<br />
This is joint work with Spencer Unger.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110512&date=2017-08-25