For more information please visit our website: http://scgp.stonybrook.edu/archives/17921

4:00pm Minicourse in Real Enumerative Geometry: V.M.Kharlamov - Real Algebraic Enumerative Geometry: Invariant Counts and TheirQualitative Properties

**Where:** Math Tower P-131**When:** Mon, May 1 4:00pm — 5:00pm

**Title:** Real Algebraic Enumerative Geometry: Invariant Counts and Their

Qualitative Properties

**Speaker:** V.M.Kharlamov [Stony Brook]

**Abstract:** In this lecture we will discuss in details more the solution of the second of the counting problems introduced in the first lecture, that is counting of real rational curves interpolating real points on K3 surfaces.

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Qualitative Properties

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4:00pm Analysis Student Seminar: TBA

**Where:** Math Tower 5-127**When:** Mon, May 1 4:00pm — 5:00pm

**Title:** TBA

**Speaker:** TBA [Stony Brook]

**Abstract:**

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1:00pm **SCGP:** SCGP Weekly Talk: Viatcheslav Kharlamov

**Where:** SCGP 102**When:** Tue, May 2 1:00pm — 2:00pm

**Title:** Deformation classification of real non-singular cubic 3-folds with marked real line.

**Abstract:** Over the complex field such a classification is well known: all the pairs (non-singular cubic 3-fold, a marked line) are deformation equivalent. As often, over the real field the picture is more diverse. Already non-singular cubic 3-folds themselves form 9 deformation classes. To give the answer to the problem with lines involved, we will discuss a natural correspondence between real cubic 3-folds and real plane quintics. The lines on a non-singular cubic 3-fold form a non-singular surface, called the Fano surface of the cubic. The classification of pairs (cubic 3-fold, marked line) is based on the study of the monodromy action on the set of real components of Fano surfaces. Here, we will use old

results by B.~Segre on monodromy of real lines on real cubic surfaces.

Hashtag: #weeklytalk

results by B.~Segre on monodromy of real lines on real cubic surfaces.

Hashtag: #weeklytalk

2:30pm **SCGP:** Topology and Symplectic Geometry Seminar: Francisco Torres de Lizaur

**Where:** SCGP 313**When:** Tue, May 2 2:30pm — 3:30pm

**Title:** Emergence of topological structures in high-energy eigenfunctions of Dirac operators

**Abstract:** We will introduce some techniques to address the following question: what type of topological structures emerge in the nodal sets of eigenfunctions of elliptic operators on compact manifolds? To illustrate these ideas, we will show that, for an infinite number of eigenfunctions of the Dirac operator on the round 3-sphere and the flat 3-torus, any knot and link type arises as nodal set of the spinor components. These structures appear at small scales and sufficiently high energies.

2:30pm Special Seminar in Algebraic Geometry: Andrea Appel - Monodromy of the Casimir connection and Coxeter categories

**Where:** Math Tower P-131**When:** Tue, May 2 2:30pm — 3:30pm

**Title:** Monodromy of the Casimir connection and Coxeter categories

**Speaker:** Andrea Appel [University of Southern California]

**Abstract:** A Coxeter category is a braided tensor category which carries an action of a generalized braid group $B_W$ on its objects. The axiomatic of a Coxeter category and the data defining the action of $B_W$ are similar in flavor to the associativity and commutativity constraints in a monoidal category, but are related to the coherence of a family of fiber functors. We will show how to construct two examples of such structure on the integrable category $\mathcal{O}$ representations of a symmetrisable Kac-Moody algebra $\mathfrak{g}$, the first one arising from the quantum group $U_{\hbar}\mathfrak{g}$, and the second one encoding the monodromy of the KZ and Casimir connections of $\mathfrak{g}$. The rigidity of this structure, proved in the framework of PROP categories, implies in particular that the monodromy of the Casimir connection is given by the quantum Weyl group operators of $U_{\hbar}\mathfrak{g}$. This is a joint work with Valerio Toledano Laredo.

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4:00pm Geometry/Topology Seminar: Kevin Payne - Comparison principles for elliptic branches of fully nonlinear PDE

**Where:** Math Tower P-131**When:** Tue, May 2 4:00pm — 5:30pm

**Title:** Comparison principles for elliptic branches of fully nonlinear PDE

**Speaker:** Kevin Payne [University of Milan]

**Abstract:** We will present a recent approach to treating the validity of comparison principles for weak solutions of scalar second order PDE of the form F(x,u(x),Hu(x)) = 0 under non standard structural conditions on F, where Hu is the Hessian of u. In particular, F(x,r,A) need not be globally monotone in r and A, which are the typical requirements for the application of maximum principle techniques in the absence of a variational structure. One exploits Krylovs notion [Trans AMS95] of elliptic branches to replace the PDE with a differential inclusion involving a certain set-valued map. A natural notion of admissible viscosity solution for the differential inclusion can be captured in terms of subaffine functions and the notion of duality of Harvey and Lawson [Comm. Pure Appl. Math09]. We will discuss these notions and show how to determine structural conditions on F which ensure that the associated set-valued map is sufficiently regular to yield the desired comparison principle. Time permitting, we will also describe how one can use maximum principle methods for treating principal eigenvalues of elliptic branches of fully nonlinear operators such as the k-Hessian on suitably convex domains. This is a joint work with Marco Cirant (Universit di Padova) and Isabeau Birindelli (Sapienza Universit di Roma)

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11:00am **SCGP:** Mini Course: Modern Fluid Mechanics: From viscous electronics in graphene to conformal invariance and anomalies in turbulence

**Where:** SCGP 313**When:** Wed, May 3 11:00am — 12:30pm

**Title:** Two-dimensional turbulence, inverse cascades and conformal invariance.

1:00pm Graduate Student Seminar: Matt Lam - TBA

**Where:** Math Tower P-131**When:** Wed, May 3 1:00pm — 2:00pm

**Title:** TBA

**Speaker:** Matt Lam [Stony Brook]

**Abstract:** TBA

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2:30pm **YITP:** joint pheno seminar at BNL - Tim Tait

**When:** Wed, May 3 2:30pm — 3:30pm

2:30pm Mini Course / Dynamics Learning Seminar: Anatoly Vershik - The metrics in ergodic theory; mm-spaces and scaling entropy

**Where:** Math Tower P-131**When:** Wed, May 3 2:30pm — 3:30pm

**Title:** The metrics in ergodic theory; mm-spaces and scaling entropy

**Speaker:** Anatoly Vershik [Petersburg Mathematics Institute]

**Abstract:** 1. Measure-metric spaces (mm-spaces), admissible metrics on the measure space; the theorem of classifications (Gromov-Vershik).

2.Scaling entropy, independence of metric. Examples and applications in terms of adic transformations.

3.Metric hyperbolicity and problems.

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2.Scaling entropy, independence of metric. Examples and applications in terms of adic transformations.

3.Metric hyperbolicity and problems.

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4:00pm Algebraic geometry seminar: Zhiwei Yun - Spectral decomposition in Betti geometric Langlands

**Where:** Math Tower P-131**When:** Wed, May 3 4:00pm — 5:30pm

**Title:** Spectral decomposition in Betti geometric Langlands

**Speaker:** Zhiwei Yun [Yale U]

**Abstract:** This is joint work with David Nadler. We consider a variant of the geometric Langlands conjecture, which is expected to be of topological nature. It relates constructible sheaves on the moduli space of G-bundles on an algebraic curve (with an important condition on the singular support of the constructible sheaves) to quasi-coherent sheaves on certain character varieties of the dual group. We show that the latter category acts on the former, hence establishing a spectral decomposition of automorphic sheaves in this setting. There is a formal analogy of our result with Vincent Lafforgue's work on the classical Langlands correspondence over a function field.

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1:00pm **SCGP:** Topology and Symplectic Geometry Seminar: Roger Casals (MIT)

**Where:** SCGP 313**When:** Thu, May 4 1:00pm — 2:00pm

**Title:** Differential Algebra of Cubic Graphs

**Abstract:** In this talk we will associate a combinatorial dg-algebra to a cubic planar graph. This algebra is defined by counting binary sequences, which we introduce, and we shall provide explicit computations. From there we study the Legendrian surfaces behind these combinatorial constructions, including Legendrian surgeries, the count of Morse flow trees involved in contact homology, and discuss the relation to microlocal sheaves. Time permitting, I will explain a connection to spectral networks.

12:00pm Grad / Postdoc Professional Development Seminar: Claude LeBrun - 10 things I wish I had known as a graduate student

**Where:** Math Tower P-131**When:** Fri, May 5 12:00pm — 1:30pm

**Title:** 10 things I wish I had known as a graduate student

**Speaker:** Claude LeBrun [Stony Brook]

**Abstract:** Get some useful advice from the (outgoing) graduate director during our last meeting this semester. As always, there will be pizza!

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2:30pm Dynamical Systems Seminar: Christian Wolf - On computability of rotation sets and their entropy

**Where:** Math Tower P-131**When:** Fri, May 5 2:30pm — 3:30pm

**Title:** On computability of rotation sets and their entropy

**Speaker:** Christian Wolf [CUNY]

**Abstract:** Given a continuous dynamical system f:X→ X on a compact metric space X and a m-dimensional continuous potential Φ = (φ1, ..., φm):X→ R, the generalized rotation set Rot(Φ) is defined as the set of all μ-integrals of Φ, where μ runs over all invariant probability measures. Analogously to the classical entropy of f, one can associate to each w ∈ Rot(Φ) the localized entropy H(w) at w. In this talk, we consider the question concerning the computability of rotation sets and localized entropy. We present positive results for shift maps and interior points of the rotation set. We also show that the situation is more complicated when dealing with points at the boundary of the rotation set. This is a joint work with Michael Burr and Martin Schmoll.

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4:00pm Geometric Analysis Learning Seminar: Fangyu Zou - TBA

**Where:** P-131 Math Tower**When:** Fri, May 5 4:00pm — 6:00pm

**Title:** TBA

**Speaker:** Fangyu Zou [Stony Brook]

**Abstract:**

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For more information please visit: http://scgp.stonybrook.edu/archives/18446