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--- seminars:topsem [2025/08/22 11:39]
lruffoni
+++ seminars:topsem [2025/10/13 13:49] (current)
lruffoni
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 <select id="setit" style="color: #0000FF" size="1" name="test">
 <option value="">Previous seminars</option>
+    <option value="http://www2.math.binghamton.edu/p/seminars/topsem/topsem_spring2025">Spring 2025</option>
     <option value="http://www2.math.binghamton.edu/p/seminars/topsem/topsem_fall2024">Fall 2024</option>
     <option value="http://www2.math.binghamton.edu/p/seminars/topsem/topsem_spring2024">Spring 2024</option>
@@ Line 37: / Line 38: @@
 ====== Fall 2025 ======
-  * **August 28th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
+  * **August 28th** \\ Speaker: ** Cary Malkiewich (Binghamton) ** \\ Title: ** Higher scissors congruence
+ ** <WRAP box>// Abstract: // Scissors congruence is the study of polytopes, up to the relation of cutting into finitely many pieces and rearranging the pieces. In the 2010s, Zakharevich defined a "higher" version of scissors congruence, where we don't just ask whether two polytopes are scissors congruent, but also how many scissors congruences there are from one polytope to another.
-  * **September 4th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
+Zakharevich's definition is a form of algebraic K-theory, which is famously difficult to compute, but I describe some recent work that makes these calculations possible, at least for low-dimensional geometries. This allows us to compute the homology of the group of cut-and-paste operations in new cases, including the group of interval exchange transformations, and a new proof of Szymik and Wahl's theorem that Thompson's group V is acyclic.
-  * **September 11th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
+Much of this talk is based on joint work with Anna-Marie Bohmann, Teena Gerhardt, Mona Merling, and Inna Zakharevich, and also with Alexander Kupers, Ezekiel Lemann, Jeremy Miller, and Robin Sroka. \\ </WRAP>
-  * **September 18th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
+  * **September 4th** \\ Speaker: ** Liz Tatum (Rochester) ** \\ Title: ** Some applications of equivariant Brown-Gitler spectra ** <WRAP box>// Abstract: //  In the 1980s, Mahowald and Kane used integral Brown-Gitler
+spectra to construct splittings of the cooperations algebras for ko,
+connective real k-theory, and ku, connective complex k-theory. These
+splittings helped make it feasible to do computations using the ko- and
+ku-based Adams spectral sequences.
-  * **September 25th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
+These spectral sequences have proven to be powerful tools for better understanding the structure of the stable homotopy groups of the sphere,  with a variety of interesting applications. For example, Mahowald used them to verify the Telescope Conjecture at height one, and Gonzalez later used them to classify stunted lens spaces.
+In this talk, I will discuss progress towards developing analogues of these tools in the C_2 equivariant setting. In particular, Guchuan Li, Sarah Petersen, and I have constructed models for C_2-equivariant analogues of the integral Brown-Gitler spectra, and used them to construct an analogue of the ku-splitting. \\ </WRAP>
-  * **October 2nd** \\ No seminar \\
+  * **September 18th** \\ Speaker: **Lorenzo Ruffoni (Binghamton) ** \\ Title: **A Pontryagin sphere at infinity in real hyperbolic space ** <WRAP box>// Abstract: // Given a discrete group of isometries of hyperbolic space, we can look at its limit set, i.e., the set of accumulation points of its orbits on the sphere at infinity. This is a compact metric space embedded in the sphere at infinity, and it often displays interesting geometric and topological features that can reveal algebraic information about the group itself.
+In this talk, first we will discuss the general theory and present classical examples of limit sets, including some simple fractals (Cantor set, Sierpinski carpet). Then, we will present the construction of groups whose limit set is a Pontryagin sphere. These groups are obtained as reflection groups, and the construction is based on the existence of certain right-angled hyperbolic polyhedra. This is joint work with S. Douba, G.-S. Lee, and L. Marquis. \\ </WRAP>
-  * **October 9th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
+  * **October 9th** \\ Speaker: ** Liam Keenan (Brown) ** \\ Title: ** On products of skeleta ** <WRAP box>// Abstract: // Given simplicial complexes, X and Y, a classical result of Eilenberg and Zilber tells us that the complex of integral chains on the product, X x Y, is quasi-isomorphic to the tensor product of complexes associated to X and Y. Their result relies on the basic observation that the product of an n-simplex with an m-simplex, can be built by gluing together simplices of dimension (n+m). Remarkably, this basic observation has much farther reaching-consequences than one might expect. In joint work with Maximilien Peroux, we showed that whenever you have two objects, X and Y, built up out of simplicies, the skeletal filtrations of X and Y can always be related to the skeletal filtration of X x Y, in an entirely canonical fashion. I will introduce this circle of ideas, explain my work with Peroux, and discuss its relation with the Dold-Kan correspondence. \\ </WRAP>
-  * **October 16th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
+  * **October 14th (Tuesday 1:30-2:30pm -- cross-listed from the [[https://www2.math.binghamton.edu/p/seminars/comb/start|Combinatorics Seminar]])** \\ Speaker: ** Lee Kennard (Syracuse) ** \\ Title: ** Regular Matroids and Torus Representations ** <WRAP box>// Abstract: // Recent work with Michael Wiemeler and Burkhard Wilking presents a link between arbitrary finite graphs and torus representations all of whose isotropy groups are connected. The link is via combinatorial objects called regular matroids, which were classified in 1980 by Paul Seymour. We then apply Seymour’s deep result to classify and to compute geometric invariants of this class of torus representations.
+The applications to geometry are significant. A highlight of our analysis of these representations is the first proof of Hopf’s 1930s Euler Characteristic Positivity Conjecture for metrics invariant under a torus action where the torus rank is independent of the manifold dimension. \\ </WRAP>
+  * **October 16th** \\ Speaker: ** John Abou-Rached (Binghamton) ** \\ Title: ** Integral models for non-Shimura curves and the Eichler-Shimura congruence relation ** <WRAP box>// Abstract: // We construct integral models for an infinite family of algebraic curves that includes noncongruence modular curves, as well as curves whose uniformizers are non-arithmetic Fuchsian groups. Most of these curves are not Shimura curves. We affirm a conjecture of Mukamel that the set of primes of good reduction of such curves have arithmetic significance and obtain an explicit description of this set. We conjecture that a version of Deligne-Rapoport's study of the reduction of modular curves holds in this context, and conjecture that a version of the Eichler-Shimura congruence relation holds in this setting, in resonance with Shimura curves. \\ </WRAP>
   * **October 23th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
-  * **October 30th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
+  * **October 30th** \\ Speaker: ** Tam Cheetham-West (Yale) ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
-  * **November 6th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
+  * **November 6th** \\ Speaker: ** Genevieve Walsh (Tufts) ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
-  * **November 13th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
+  * **November 13th** \\ Speaker: ** Maximilien Peroux (Michigan State University) ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
-  * **November 20th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
+  * **November 20th** \\ Speaker: ** David Chan (Michigan State University) ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
   * **November 27th** \\ No seminar  \\
-  * **December 4th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
+  * **December 4th** \\ Speaker: **Hongbin Sun (Rutgers) ** \\ Title: ** ** <WRAP box>// Abstract: //  \\ </WRAP>
-====== Spring 2025 ======
-  * **January 23rd** \\ Organizational meeting, meet in WH 100E at 2:50pm
-  * **January 30th** \\ Speaker: **Matthew Zaremsky** (University at Albany) \\ Title: **Progress around the Boone-Higman conjecture** <WRAP box>// Abstract: // The Boone-Higman conjecture (1973) predicts that every finitely generated group with solvable word problem embeds in a finitely presented simple group. There has been a flurry of recent activity around this conjecture, in particular relating it to the family of so called twisted Brin-Thompson groups. In this talk I will give some background on the conjecture, give a gentle introduction to twisted Brin-Thompson groups, and then discuss various recent results of mine, including some joint with combinations of Jim Belk, Collin Bleak, Francesco Fournier-Facio, James Hyde, and Francesco Matucci. \\ </WRAP>
-  * **February 6th** \\ Problem session \\
-  * **February 13th** \\ No seminar \\
-  * **February 20th** \\ No seminar \\
-  * **February 27th** \\ Speaker: **Valentina Zapata Castro** (University of Virginia) \\ Title: **Monoidal complete Segal spaces** <WRAP box>// Abstract: // Viewing a monoid as a category with a single object allows us to encode the binary operation using the properties of composition and associativity inherent in any category. In this talk, we use this idea to explore the relationship between $(\infty,1)$-categories with a monoidal structure and $(\infty,2)$-categories with one object. This exploration relies on the model structure of simplicial and $\Theta_2$-spaces.  The talk is designed to be self-contained, requiring no prior knowledge of the aforementioned categories. \\ </WRAP>
-  * **March 6th** \\ Speaker: **Inhyeok Choi** (Cornell University) \\ Title: **Genericity of pseudo-Anosovs and quasi-isometries** <WRAP box>// Abstract: // In this talk, I will explain a recent result that pseudo-Anosov mapping classes are generic in every Cayley graph of mapping class groups. If time permits, I will also explain why this strategy goes well with quasi-isometries and implies genericity of Morse elements for groups quasi-isometric to (many) 3-manifold groups and special cubical groups. \\ </WRAP>
-  * **March 13th** \\ Spring break
-  * **March 20th** \\ Peter Hilton Memorial Lecture
-  * **March 27th** \\ Speaker: **Colby Kelln** (Cornell University) \\ Title: **Coning off a hyperbolic manifold with totally geodesic boundary** <WRAP box>// Abstract: // Let $M$ be a compact hyperbolic manifold with totally geodesic boundary. If the injectivity radius of $\partial M$ is larger than an explicit function of the normal injectivity radius of $\partial M$, we show there is a negatively curved metric on the space obtained by coning each boundary component of $M$ to a point. Moreover, we give explicit geometric conditions under which a locally convex subset of $M$ gives rise to a locally convex subset of the cone-off. Group-theoretically, we conclude that the fundamental group of the cone-off is hyperbolic and the $\pi_1$-image of the locally convex subset is a quasi-convex subgroup. \\ </WRAP>
-  * **April 3rd** \\ Speaker: **Theodore Weisman** (University of Michigan) \\ Title: **Anosov representations of cubulated hyperbolic groups** <WRAP box>// Abstract: // An Anosov representation of a hyperbolic group $\Gamma$ is a representation which quasi-isometrically embeds $\Gamma$ into a semisimple Lie group - say, SL(d, R) - in a way which imitates the behavior of a convex cocompact group acting on a hyperbolic metric space. It is unknown whether every linear hyperbolic group admits an Anosov representation. In this talk, I will discuss joint work with Sami Douba, Balthazar Flechelles, and Feng Zhu, which shows that every hyperbolic group that acts geometrically on a CAT(0) cube complex admits a 1-Anosov representation into SL(d, R) for some d. Mainly, the proof exploits the relationship between the combinatorial/CAT(0) geometry of right-angled Coxeter groups and the projective geometry of a convex domain in real projective space on which a Coxeter group acts by reflections. \\ </WRAP>
-  * **April 10th** \\ Speaker: **Marco Volpe** (University of Toronto) \\ Title: **Fiberwise simple homotopy theory** <WRAP box>// Abstract: // Simple homotopy theory is, roughly speaking, the study of finite CW-complexes up to collapses and expansions. From its early stages, it has been observed that simple homotopy types are deeply connected to K-theory. This connection is realized through Wall's finiteness obstruction for finitely dominated complexes and the Whitehead torsion of a homotopy equivalence between finite complexes. One of Waldhausen's main contributions ('83) to simple homotopy theory was to incorporate both Wall's obstruction and the Whitehead torsion in the study of assembly maps in K-theory. Later on, Dwyer-Weiss-Williams ('03) have introduced "fiberwise" assembly maps associated to fibrations over a fixed base space, thereby providing a framework for understanding simple homotopy types varying in families.
-In this talk, we introduce a novel perspective on fiberwise assembly maps, developed via the infinity-category of sheaves of spectra on a topological space. Using this approach, we are able to simultaneously generalize both the recently announced (but as yet unpublished) work of Bartels-Efimov-Nikolaus and the topological Dwyer-Weiss-Williams index theorem ('03).
-This is a joint work with Maxime Ramzi and Sebastian Wolf. \\ </WRAP>
-  * **April 17th** \\ Speaker: **Sayantika Mondal** (CUNY) \\ Title: **Distinguishing filling curves via designer metrics** <WRAP box>// Abstract: // There are many topological invariants one can associate with homotopy classes of closed curves. These include algebraic and geometric self-intersection number, intersection with curves in a class of curves (for example, simple ones), the Goldman bracket, complementary component types of a curve, mapping class group stabilizers of a curve, and many others. How these invariants interact and determine the curve type (mapping class group orbit) is an active area of research today. In this talk, we focus on the so called inf invariant (shortest length metric) associated to a filling curve, its relationship with the geometric self-intersection number, and its relation to the optimal metric that is tailored to produce the minimum length. While clearly the geometric self-intersection number is a type invariant, we address whether the inf invariant can distinguish between curves that have the same self-intersection. This is joint work with Ara Basmajian. \\ </WRAP>
-  * **April 24th** \\ Speaker: **Kasia Jankiewicz** (UC Santa Cruz / IAS) \\ Title: **Cubical quotients of cubical nonproduct groups** <WRAP box>// Abstract: // Burger-Mozes constructed examples of simple groups acting geometrically on a CAT(0) complex, which is a product of trees. As a counterpoint, we prove that every group acting geometrically on a CAT(0) cube complex which is not a product, admits a nontrivial quotient which also admits a geometric action on a CAT(0) cube complex. Our construction relies on the cubical version of small cancelation theory. This is joint work with M. Arenas and D. Wise. \\ </WRAP>
-  * **Tuesday April 29th, 1:15-2:15 pm** (joint with the [[https://www2.math.binghamton.edu/p/seminars/comb/start|Combinatorics Seminar]]) \\ Speaker: **Leo Jiang** (Toronto) \\ Title: **Topology of Real Matroid Schubert Varieties** <WRAP box>// Abstract: // Every linear representation of a matroid determines a matroid Schubert variety whose geometry encodes combinatorics of the matroid. When the representation is over the real numbers, we study the topology of the real points of the variety. Our main tool is an explicit cell decomposition, which depends only on the oriented matroid structure and can be extended to define a combinatorially interesting topological space for any oriented matroid. This is joint work with Yu Li. \\ </WRAP>
-  * **May 1st - DOUBLE HEADER** \\ Speaker: **Chaitanya Tappu** (Cornell University) -- **2:50-3:50pm** \\ Title: **Contractibility of the marked moduli space** <WRAP box>// Abstract: // We prove that the marked moduli space of any infinite type surface is contractible. The marked moduli space of an infinite type surface (equipped with an action of the big mapping class group) is introduced as the generalisation of the usual Teichmüller space of a finite type surface. This result is analogous to that of Douady--Earle, who proved that the (quasiconformal) Teichmüller space of an arbitrary Riemann surface, whether of finite or infinite type, is contractible. Even though the marked moduli space reduces to the Teichmüller space in case the surface is of finite type, it is quite distinct from the Teichmüller space in case the surface is of infinite type. Nevertheless, we are able to adapt the Douady--Earle proof to the setting of the marked moduli space. A key difference is that in this setting, we use a Fréchet space topology on the vector space of (-1, 1)-forms (that is, Beltrami forms), rather than the usual Banach space topology.  \\ </WRAP>  Speaker: **Filippo Calderoni** (Rutgers) -- **4:15 - 5:15pm** \\ Title: **Groups, orders, and dynamics: a new perspective** <WRAP box>// Abstract: // A countable group G is said to be left-orderable if it admits a total order which is invariant under left multiplication, or, equivalently, if G admits a faithful action by orientation preserving homeomorphisms on the real line.
-There is a beautiful connection between the algebraic properties of a left-orderable group G and the conjugacy action on LO(G), the compact Hausdorff space of all left-orders supported by G. In this talk I will survey some results towards characterizing those left-orderable groups such that the orbit space of LO(G) modulo conjugacy is trivial from the viewpoint of descriptive set theory. \\ </WRAP>

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