Seminar Calendar
for events the week of Wednesday, January 28, 2015.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, January 26, 2015

Symplectic & Poisson Geometry Seminar
12:00 pm   in 341 AH,  Monday, January 26, 2015
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Submitted by jawatts.
Daniele Sepe (Universidade Federal Fluminense)
Singular integral affine structures and focus-focus singularities
Abstract: The classification of completely integrable Hamiltonian systems is a driving question in Hamiltonian mechanics and symplectic geometry as these can be thought of as (examples of) complexity zero Hamiltonian R^n-actions on symplectic 2n-dimensional manifolds. Away from the locus of singularities (which, mechanically, correspond to equilibria of the system), Duistermaat's approach has revealed the importance of integral affine structures in the study of such systems. A natural question is whether the relation between integral affine geometry and completely integrable Hamiltonian systems can be extended to singularities, which contain important geometric and dynamical information. The aim of this talk is to present a differential-geometric notion of singular integral affine structures by illustrating its role in the classification of neighbourhoods of focus-focus singular fibres, which are analogous to nodal fibres in Lefschetz fibrations. This is ongoing joint work with Rui Loja Fernandes.

Operator Algebra Learning Seminar
5:00 pm   in 241 Altgeld Hall,  Monday, January 26, 2015
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Submitted by mjunge.
Minyu Zhao (UIUC)
Khintchine inequalities
Abstract: Organization meeting and intro to (nc) Khintchine inequalities

Tuesday, January 27, 2015

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, January 27, 2015
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Submitted by cmalkiew.
Saul Glasman   [email] (MIT)
The Hodge filtration on topological Hochschild homology
Abstract: In the 80s, many mathematicians independently defined a filtration on the Hochschild homology of a commutative algebra A that recovers the Hodge filtration of the de Rham complex of A in the case where A is a smooth Q-algebra. The subject of this talk is a refinement of this to a filtration by spectra of the topological Hochschild homology of a commutative ring spectrum. I'll give some motivation for this filtration and describe its construction and properties, and then I'll discuss how to lift it to a filtration of topological cyclic homology using techniques of equivariant stable homotopy theory.

Geometry, Groups and Dynamics/GEAR Seminar
1:00 pm   in Altgeld Hall 243,  Tuesday, January 27, 2015
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Submitted by kapovich.
Funda Gultepe (UIUC Math)
Fully irreducible Automorphisms of the Free Group via Dehn twisting in $\sharp_k(S^2 \times S^1)$
Abstract: By using a notion of a geometric Dehn twist in $\sharp_k(S^2 \times S^1)$, we prove that when projections of two $Z$-splittings to the free factor complex are far enough from each other in the free factor complex, Dehn twist automorphisms corresponding to the $Z$ splittings generate a free group of rank $2$. Moreover, every element from this free group is either conjugate to a power of one of the Dehn twists or it is a fully irreducible outer automorphism of the free group. View lecture at http://youtu.be/9nSWL4g19lk

Graph Theory and Combinatorics Seminar
3:00 pm   in Altgeld Hall 241,  Tuesday, January 27, 2015
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Submitted by molla.
Douglas B. West   [email] (Zhejiang Normal University and UIUC Math)
Decomposition of Sparse Graphs into Forests: The Nine Dragon Tree Conjecture for $k\le2$.
Abstract: For a loopless multigraph $G$, the *fractional arboricity* $Arb(G)$ is the maximum of $|E(H)|/(|V(H)|-1)$ over all subgraphs $H$ with at least two vertices. Generalizing the Nash-Williams Arboricity Theorem, the Nine Dragon Tree Conjecture asserts that if $Arb(G) <= k + d/(k+d+1)$, then G decomposes into $k+1$ forests with one having maximum degree at most $d$. The conjecture, which is sharp, was previously proved for $d=k+1$ and for $k=1$ when $d\le6$. We prove it for all $d$ when $k \le 2$, except for $(k,d)=(2,1)$. (Joint work with Min Chen, Seog-Jin Kim, Alexandr Kostochka, and Xuding Zhu.)

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, January 27, 2015
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Submitted by katz.
Sheldon Katz (Illinois Math)
Motivic Stable Pair Invariants and K3 Surfaces
Abstract: This talk focuses on the conjectural motivic extension, developed jointly with Klemm and Pandharipande, of the results of Pandharipande and Thomas which prove the KKV formula for enumerative invariants on K3 surfaces. Background will be given on stable pair invariants and motivic invariants. Reference: http://arxiv.org/abs/1407.3181

Mathematics Colloquium - Special Lecture 2014-15
4:00 pm   in 245 Altgeld Hall,  Tuesday, January 27, 2015
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Submitted by seminar.
Shu Li (University of Waterloo)
Insurance risk processes with dynamic changes
Abstract: In this talk, we analyze two insurance risk processes which allow dynamic adjustments based on their surplus experience. First, we consider a risk model with varying premiums, where the insurer's decision of the next period's premium rate is based on the surplus increments between successive random review times. Under certain assumptions of the review time and claim arrival process, we derive a matrix-form defective renewal equation for the Gerber-Shiu function, as well as an explicit expression for the joint density of the surplus prior to ruin and the deficit at ruin. Numerical examples are later considered to evaluate certain ruin-related quantities and some risk management conclusions are made. Second, we analyze a drawdown-based regime-switching (DBRS) Levy insurance model in which the underlying drawdown process is used to model an insurer's level of financial distress over time and to trigger regime-switching transitions. By some analytical arguments, we derive explicit formulas for the two-sided exit problem and further examine the conditions under which the survival probability is not trivially zero (i.e., the positive security loading conditions). As a special case of the DBRS model, we investigate a jump diffusion model with regime-switching premiums and build connections with other existing risk models in the literature.

Graduate Student Analysis Seminar
4:00 pm   in 243 Altgeld Hall,  Tuesday, January 27, 2015
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Submitted by ackrmnn2.
Interest and Planning Meeting
Abstract: We will be scheduling talks for this semester, making an email list, and possibly going out for dinner afterwards. All fields of analysis including, but not limited to functional analysis, complex analysis, geometric analysis, probability, differential equations and ergodic theory are welcome. If you are unable to attend the meeting, but would like to give a talk please email Colleen Ackermann (ackrmnn2@illinois.edu) with a list of preferred weeks. Younger grad students who have an interest in analysis, but may not feel ready to give a talk are also more than welcome to attend.

Thursday, January 29, 2015

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, January 29, 2015
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Submitted by astraub.
Sunil Chebolu   [email] (Illinois State University)
When is the multiplicative group of a field indecomposable?
Abstract: Recall that an abelian group is said to be indecomposable if it cannot be written as a direct sum of two non-trivial subgroups. Let F be a field and let F^* denote the multiplicative group of F. The problem we investigate is the following. When is F^* an indecomposable abelian group? We will solve this problem when the characteristic of F is not equal to 2. The answer involves Mersenne and Fermat primes, and one solution to this problem involves the famous Catalan's conjecture. We also have some partial results when the characteristic of the field is 2. I will discuss these results which are in joint work (arXiv:1407.3481) with Keir Lockridge.

Geometry, Groups and Dynamics/GEAR Seminar
1:00 pm   in Altgeld Hall 243,  Thursday, January 29, 2015
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Submitted by kapovich.
Nathan Dunfield (UIUC Math)
Certifying the Thurston norm via twisted homology
Abstract: From the very beginning of 3-manifold topology, a fundamental task has been to find the simplest surface in a given 2-dimensional homology class, e.g. the Seifert genus of a knot in the 3-sphere. The behavior of the minimal topological complexity as the homology class varies is encapsulated in the Thurston norm. In this talk, I will discuss tools for proving that a particular surface has minimal genus. These are generalizations of the classical Alexander polynomial, but are defined using homology with coefficients twisted by some finite-dimensional representation of the fundamental group of the manifold. I will discuss recent work with Ian Agol on situations where using representations coming from hyperbolic geometry suffices to provide such certificates. If time permits, I will sketch how all of this relates to fundamental questions about the computational complexity of finding the Thurston norm. Only basic facts about manifolds and homology will be assumed. View lecture at http://youtu.be/b7a-WXpNLAQ

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, January 29, 2015
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Submitted by tumanov.
Fabrice Baudoin (Purdue University)
Sub-Riemannian isoperimetric inequalities on totally geodesic foliations
Abstract: In this talk I will present some joint works with Bumsik Kim concerning isoperimetric inequalities on sub-Riemannian manifolds that come from a totally geodesic Riemannian foliation.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, January 29, 2015
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Submitted by mastroe2.
Organizational Meeting

Mathematics Colloquium - Special Lecture 2014-15
4:00 pm   in 245 Altgeld Hall,  Thursday, January 29, 2015
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Submitted by seminar.
Yang Shen (University of New South Wales)
TBA