The Simons Center for Geometry and Physics (SCGP) is honored to present seventy works by the world-renowned Dutch artist Maurits Cornelis Escher (1898-1972). The art will be on view at the Simons Center Gallery from October 11 through November 19, 2021.

M.C. Escher crafted an extraordinary graphical language inspired by mathematics, puzzles, and patterns. His art explores mathematical operations and ideas expressed in infinity, symmetry, geometry, tessellated surfaces, improbable architectural perspectives, and more.

In addition to featuring Escher’s iconic prints such as* Relativity*, the Simons Center Gallery shall host some of his lesser-known early work focusing on nature and landscape, many of which bear the harbinger of mathematical forms and morphing shapes seen in later work.

Escher was a consummate printmaker; a master craftsperson. He used three different, albeit related, print techniques: 1) relief printing: woodcut, linocut and wood engraving, 2) intaglio printing: etching and mezzotint, and 3) planographic printmaking: lithograph. All three print methods utilized by Escher are showcased at the Simons Center Gallery.

According to most accounts, Escher made his first print when he was seventeen years old, and his last when he was seventy-one. During his lifetime, Escher created 448 prints and more than 2000 drawings and sketches, including watercolors.

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The Simons Center for Geometry and Physics is a research center devoted to furthering fundamental knowledge in geometry and in theoretical physics, especially knowledge at the interface of these two disciplines. As part of the SCGP’s 10th anniversary, the Center is delighted to host this special exhibition. Originally scheduled for 2020, the exhibit will open fall, 2021.

http://scgp.stonybrook.edu/escher

- 2:00pm - 3:00pm
- in SCGP - 102

Talks by postdoctoral scholars at the SCGP, Stony Brook Mathematics department, and the IMS introducing the foundational concepts and questions in their fields. The talks will be at the level accessible to all other postdocs in all fields of mathematics. Organized by Sam Grushevsky. October 18th - December 6th.

http://scgp.stonybrook.edu/archives/35014

- 1:00pm - 2:00pm
- in SCGP Lecture Hall - 102

**Speaker:** John Pardon, Princeton University**Title:** Enough vector bundles on orbispaces**Abstract:** An orbispace is a "space" which is locally the quotient of a topological space by a continuous action of a finite group. Familiar examples of orbispaces include orbifolds, (the analytifications of) Deligne--Mumford stacks over C, and moduli spaces of solutions to elliptic partial differential equations, as they appear in low-dimensional and symplectic topology. The fibers of a vector bundle over an orbispace are representations of its stabilizer groups. When do there exist vector bundles all of whose fiber representations are faithful? This condition is called having "enough" vector bundles, and plays an important role in the stable homotopy theory of orbispaces. In particular, it implies a Spanier--Whitehead duality functor in a certain stable homotopy category of orbispaces and a Pontryagin--Thom isomorphism for orbifold bordism groups.

- 4:30pm - 5:30pm
- in Online

**Title:** TBA **Speaker:** Xi Sisi Shen [Columbia University] **Abstract:**

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- 1:30pm - 2:30pm
- in SCGP 102

**Speaker:** Thomas Vandermeulen**Title:** Extended Symmetries and Anomaly Resolution in Orbifolds**Abstract:** Symmetries in quantum field theories can carry anomalies which obstruct their gauging. I will discuss a method of resolving such anomalies in two-dimensional conformal field theories by extending the symmetry group. This technique relies on the addition of trivially-acting symmetries, the study of which is known as decomposition. We will see in detail how, through decomposition, orbifolds by extended symmetries can end up equivalent to orbifolds by non-anomalous subgroups.

- 2:30pm - 3:30pm
- in Math P-131 and zoom

**Title:** The boundaries of the main hyperbolic component **Speaker:** Yusheng Luo [Stony Brook University] **Abstract:** Hyperbolic polynomials or rational maps form an open and conjecturally dense subset in the moduli space. A connected component is called a hyperbolic component. The topology of the hyperbolic compoennts has been studied extensively in various different settings. However, the boundaries of hyperbolic components and the interactions between different hyperbolic components remain very mysterious. In this talk, we will discuss how `quasi post-critically finite' degenerations of Blaschke products allows us to investigate these questions. In particular, we will use it to

1) classify geometrically finite polynomials on the boundary of the main hyperbolic component of degree d polynomials.

2) construct a self-bump on the boundary of the main hyperbolic component, and thus show the closure of the main hyperbolic component is not a manifold with boundary for degree > 3.

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- 4:30pm - 5:30pm
- in SCGP 102

**Title:** Spectral techniques in Markov chain mixing **Speaker:** Evita Nestoridi [Princeton University] **Abstract:** How many steps does it take to shuffle a deck of $n$ cards, if at each step we pick two cards uniformly at random and swap them? Diaconis and Shahshahani proved that $\frac{1}{2} n log n$ steps are necessary and sufficient to mix the deck. Using the representation theory of the symmetric group, they proved that this random transpositions card shuffle exhibits a sharp transition from being unshuffled to being very well shuffled. This is called the cutoff phenomenon. In this talk, I will explain how to use the spectral information of a Markov chain to study cutoff. As an application, I will briefly discuss the random-to-random card shuffle (joint with M. Bernstein) and the non-backtracking random walk on Ramanujan graphs (joint with P. Sarnak).

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- 2:45pm - 4:15pm
- in Math 4-130

**Title:** Closed geodesics and Frøyshov invariants of hyperbolic three-manifolds **Speaker:** Francesco Lin [Columbia University] **Abstract:** Frøyshov invariants are subtle numerical topological invariants of rational homology three-spheres derived from gradings in monopole Floer homology. In this talk I will look at their relation with invariants arising from hyperbolic geometry (such as volumes and lengths of closed geodesics), using an odd version of the Selberg trace formula and ideas from analytic number theory. In particular, for the class of minimal L-spaces, I will describe an effective procedure to compute them taking as input explicit geometric data, and show for example how this can be used to determine all the Frøyshov invariants for the Seifert-Weber dodecahedral space. This is joint work with M. Lipnowski.

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Last day students can process a withdrawal from an individual course(s) via SOLAR. "W" (withdrawal) will berecorded on transcript. Changes must be processed by 4:00 PM.

Last day to submit a Section/Credit Change Form to Office of Registrar. Changes must be processed by4:00 PM. After this date petition is required and "W" (withdrawal) will be recorded on transcript.

Last day students can select Grade/Pass/No Credit (GPNC). Changes must be processed by 4:00 PM. Non-petionable.

- 10:00am - 11:00am
- in Zoom

**Title:** Uniformization of planar domains by exhaustion **Speaker:** Kai Rajala [University of Jyvaskyla] **Abstract:** In 1908, Koebe conjectured that every subdomain of the complex plane admits a conformal map onto a circle domain. Koebe verified his conjecture for finitely connected domains, and He and Schramm for countably connected domains. We discuss the method of constructing conformal maps onto circle domains by approximating a given domain with an increasing sequence of finitely connected subdomains and considering the corresponding sequence of conformal maps onto finitely connected circle domains. We show that this method fails if one starts with an arbitrary approximation, but that it works for countably connected domains after small adjustments.

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- 11:00am - 12:00pm

**Title:** TBA **Speaker:** Kai Rajala [University of Jyvaskyla] **Abstract:**

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- 11:15am - 12:15pm
- in SCGP 102

**Speaker:** Luca Delacretaz**Title:** TBD**Abstract:** TBD

- 11:30am - 12:30pm
- in zoom

**Title:** mini-course: Dynamics of rational surface automorphisms **Speaker:** Eric Bedford [Stony Brook University] **Abstract:** This concerns the dynamics of holomorphic mappings of compact surfaces of complex dimension 2. In this series of lectures, we will explain what rational surface automorphisms are and how to discuss their dynamics.

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Students may begin to submit major/minor changes effective Spring 2022 Semester