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A live feed of seminars and special events in the upcoming week.

- February 3rd, 2014 (12:20pm - 01:30pm)
**Seminar:**CCMA Luncheon Seminar**Title:**Optimal transport theory, with some applications**Speaker:**Alessio Figalli, University of Texas at Austin**Location:**MB114**Abstract:**http://www.ma.utexas.edu/users/figalliThe optimal transportation problem consists in finding the cheapest way to transport a distribution of mass from one place to another. Surprisingly, optimal transportation has become a very powerful tool to obtain sharp geometric inequalities, such as for instance the isoperimetric or the Brunn-Minknowski inequality. In this short talk I’ll introduce the optimal transport problem and show how it can be used to prove this kind of inequalities.

- February 3rd, 2014 (02:30pm - 03:30pm)
**Seminar:**Computational and Applied Mathematics Colloquium**Title:**Stability results for functional inequalities and applications**Speaker:**Alessio Figalli, University of Texas at Austin**Location:**MB106**Abstract:**http://www.ma.utexas.edu/users/figalliGeometric and functional inequalities play a crucial role in several problems arising in the calculus of variations, partial differential equations, geometry, etc. More recently, there has been a growing interest in studying the stability for such inequalities. The basic question one wants to address is the following: suppose we are given a functional inequality for which minimizers are known. Can we prove that if a function “almost attains the equality” then it is close (in some suitable sense) to one of the minimizers? The aim of this talk is to describe some ways to attack this kind of problems, and to show some applications. The talk is intended to be accessible to graduate students.

- February 3rd, 2014 (03:35pm - 04:35pm)
**Seminar:**Dynamical systems seminar**Title:**GL(2,R) orbit closures of translation surfaces**Speaker:**Alex Wright, University of Chicago**Location:**MB114We will survey recent results towards the classification of GL(2,R) orbit closures of translation surfaces, including the technique of cylinder deformations and the author's joint results with Aulicino and Nguyen in genus 3.

- February 4th, 2014 (11:15am - 12:05pm)
**Seminar:**Combinatorics/Partitions Seminar**Title:**Congruences for Fishburn Numbers**Speaker:**James Sellers, Penn State University**Location:**MB106The Fishburn numbers, originally considered by Peter C. Fishburn, have been shown to enumerate a variety of combinatorial objects. These include unlabelled interval orders on n elements, (2+2)--avoiding posets with n elements, upper triangular matrices with nonnegative integer entries and without zero rows or columns such that the sum of all entries equals n, non--neighbor--nesting matches on [2n], a certain set of permutations of [n] which serves as a natural superset of the set of 231--avoiding permutations of [n], and ascent sequences of length n. However, as far as we know, the Fishburn numbers have not been studied from an arithmetic point of view. In this talk, we prove that the Fishburn numbers satisfy infinitely many Ramanujan--like congruences modulo certain primes p (the set of which we will easily describe in the talk). This is joint work with George Andrews.

- February 4th, 2014 (02:30pm - 03:30pm)
**Seminar:**GAP Seminar**Title:**Quantum field theory on curved Lorentzian space times**Speaker:**Nguyen Viet Dang, Universite Paris 7 and Penn State**Location:**MB106I will give an introduction to quantum field theory on curved space time, emphasizing the central notion of causality. Then I will explain the analytical problems encountered when one tries to define the quantities of interest in QFT, namely the n point functions, and how renormalization solves these analytical issues. This is ongoing project with Christian Brouder from Paris 6.

- February 4th, 2014 (02:30pm - 03:45pm)
**Seminar:**Logic Seminar**Title:**Algorithmically random probability measures**Speaker:**Quinn Culver, Notre Dame University**Location:**MB315We define a natural, computable map that associates to each real a Borel probability measure on Cantor space, so that we can talk about random measures, the images of the (ML) random reals. We show that such random measures are atomless yet mutually singular with respect to the Lebesgue measure. We show also that any two relatively random measures share a random real, yet are mutually singular. We finish with some miscellaneous results and some open questions.

- February 4th, 2014 (03:35pm - 04:25pm)
**Seminar:**Special Colloquium**Title:**Isoperimetric Inequality and Q-curvature**Speaker:**Yi Wang, Stanford University**Location:**MB114**Abstract:**http://A well-known question in differential geometry is to prove the isoperimetric inequality under intrinsic curvature conditions. In dimension 2, the isoperimetric inequality is controlled by the integral of the positive part of the Gaussian curvature. In my recent work, I prove that on simply connected conformally flat manifolds of higher dimensions, the role of the Gaussian curvature can be replaced by the Branson's Q-curvature. The isoperimetric inequality is valid if the integral of the Q-curvature is below a sharp threshold. Moreover, the isoperimetric constant depends only on the integrals of the Q-curvature. The proof relies on the theory of $A_p$ weights in harmonic analysis.

- February 4th, 2014 (03:50pm - 04:50pm)
**Seminar:**Tensor Networks and Applications Seminar**Title:**Overview of Singular Learning Theory**Speaker:**William Wright, Penn State University**Location:**MB315We will discuss the basics of statistical learning theory and address what it means for a statistical model to be singular. Next, we will outline the role of algebraic geometry in understanding the asymptotic behavior of such learning machines. With an eye toward computational complexity, we will then discuss an alternative approach to certain classes of models known as regularly parametrized models.

- February 4th, 2014 (04:40pm - 05:30pm)
**Seminar:**Special Colloquium**Title:**Rigidity of Higher Rank Abelian Actions**Speaker:**Zhiren Wang, Yale University**Location:**MB114A $Z$-action generated by a single toral automorphism is not rigid, in the sense that invariant measures and subsets can behave quite arbitrarily. However, this is not the case for generic $Z^r$-actions by toral automorphisms. In this talk, we will describe rigidity properties of algebraic $Z^r$-actions on nilmanifolds in the categories of measures, subsets and smooth structures. We show that, up to smooth conjugacy, all Anosov $Z^r$-actions without rank-one actions on tori and nilmanifolds act by automorphisms. We will also explain how one can establish similar rigidity statements for actions by higher rank lattices by studying their abelian subgroups. This talk is partially based on joint works with Aaron Brown and Federico Rodriguez Hertz.

- February 4th, 2014 (05:30pm - 06:30pm)
**Seminar:**Special Talk**Title:**Student-Focused Teaching: How to Improve Student Performance, Boost SRTEs, and Enjoy Teaching**Speaker:**Sara Jamshidi, Penn State**Location:**MB114**Abstract:**http://Classic styles of university instruction are very teacher-centric. The focus is on creating a syllabus, a series of lectures, and a set of exams. These items are typically based on what is "interesting" to the instructor. Though an old tradition, it may not be the best approach to classroom design. In this talk, I will review the basic structure of a classroom with a more student-centric perspective. The word design will have much more weight because we will compare the act of crafting a course to the act of designing a commercial product. We will ask questions about subjective elements, like student experience and perceived value of the course, as well as objective elements, like the relevancy of the course to students' future plans. By basic structure, I mean to cover goals, objectives, policies, and writing course material. Time permitting, we will also discuss student-teacher relationships--an important part of the student experience.

- February 5th, 2014 (12:05pm - 01:20pm)
**Seminar:**Geometry Luncheon Seminar**Title:**Smoothing of polyhedral space**Speaker:**Anton Petrunin, PSU**Location:**MB114: We will show that any 3-dimensional polyhedral manifold with nonnegative curvature can be approximated by Riemannian manifolds with nonnegative curvature. The proof is a compilation of results in Ricci flow and Alexandrov geometry. This is joint work with N. Lebedeva, V. Matveev and V. Shevchishin.

- February 6th, 2014 (11:15am - 12:05pm)
**Seminar:**Algebra and Number Theory Seminar**Title:**Small gaps between primes**Speaker:**James Maynard, Centre de recherches mathématiques**Location:**MB106It is believed that there should be infinitely many pairs of primes which differ by 2; this is the famous twin prime conjecture. More generally, it is believed that for every positive integer $m$ there should be infinitely many sets of $m$ primes, with each set contained in an interval of size roughly $m\log{m}$. Although proving these conjectures seems to be beyond our current techniques, recent progress has enabled us to obtain some partial results. We will introduce a refinement of the `GPY sieve method' for studying these problems. This refinement will allow us to show (amongst other things) that $\liminf_n(p_{n+m}-p_n)<\infty$ for any integer $m$, and so there are infinitely many bounded length intervals containing $m$ primes.

- February 6th, 2014 (03:35pm - 04:25pm)
**Seminar:**Department of Mathematics Colloquium**Title:**Syzygies of Veronese embeddings**Speaker:**Claudiu Raicu, Princeton University**Location:**MB114Syzygies are important classical invariants attached to algebraic varieties. They can be defined iteratively starting from the defining equations of a variety and continuing with the relations between these equations, the relations between the relations etc. In the special case of the Veronese embeddings of the projective space, the structure of syzygies is particularly rich due to the presence of a large group of symmetries. Their study can be approached through a variety of techniques, placing them at the confluence of algebraic geometry, commutative algebra, representation theory and combinatorics. I will discuss some recent results on the structure of the syzygies of Veronese embeddings, and explain how their vanishing controls the asymptotic vanishing behavior (in the sense of Ein and Lazarsfeld) of syzygies of arbitrary algebraic varieties.

- February 7th, 2014 (12:20pm - 01:10pm)
**Seminar:**Teaching Mathematics Discussion Group Seminar**Title:**Teaching with Applications**Speaker:**Attendees, Penn State**Location:**MB101To what extent should applications of mathematical techniques be included in course material? Some exclude applications while others use it as a guiding motivation. We will look at the following paper and discuss. http://www.tandfonline.com/doi/abs/10.1080/10511970508984117 Copies will be provided at the meeting.

- February 7th, 2014 (03:35pm - 04:35pm)
**Seminar:**Probability and Financial Mathematics Seminar**Title:**Gaussian Limits for A Fork-Join Network with Non-Exchangeable Synchronization in Heavy Traffic**Speaker:**Hongyuan Lu, PSU, Industr. & Manufact. Engineering**Location:**MB106We study a fork-join network of stations with multiple servers and non-exchangeable synchronization in heavy traffic under the FCFS discipline. Each arriving job forks into $K$ parallel tasks, which are processed simultaneously in $K$ parallel service stations. After service completion, each task will wait in a buffer associated with its service station for synchronization. Tasks are only synchronized if all the tasks associated with the same job are completed. We develop a new approach to show a functional central limit theorem for the number of tasks in each waiting buffer for synchronization, jointly with the number of tasks in each parallel service station and the number of synchronized jobs, under general assumptions on the arrival and service processes. Specifically, we represent the aforementioned processes as functionals of a sequential empirical process driven by the sequence of service vectors for each job's parallel tasks. As a consequence, all the limiting processes are functionals of two independent processes - the limiting arrival process and a generalized Kiefer process driven by the service vector of each job. We characterize the transient and stationary distributions of those limit processes.

- February 10th, 2014 (12:20pm - 01:30pm)
**Seminar:**CCMA Luncheon Seminar**Title:**What is weak convergence**Speaker:**Gautam Iyer, Carnegie Mellon University**Location:**MB114**Abstract:**http://www.math.cmu.edu/math/faculty/iyer.htmlI will talk about a few standard and useful results about weak convergence, some of which I will use in my colloquium talk.

- February 10th, 2014 (02:30pm - 03:30pm)
**Seminar:**Computational and Applied Mathematics Colloquium**Title:**Stirring and Mixing**Speaker:**Gautam Iyer, Carnegie Mellon University**Location:**MB106**Abstract:**http://www.math.cmu.edu/math/faculty/iyer.htmlI will talk about various ``mixing'' questions that have attracted interest recently. For instance, ``Can you stir your coffee to keep it hot for longer'', or ``How well can you stir cream into your coffee, and at what cost?''. Mathematically these questions translate into studying a negative Sobolev norm of a passively advected scalar. The study of such questions also involves very interesting connection Bressan's (still open!) rearrangement cost conjecture. I will spend most of the talk surveying recent results, and conclude with brief description of joint work with A. Kiselev, Xiaoqian Xu and myself.

- February 10th, 2014 (03:35pm - 05:35pm)
**Seminar:**Dynamical systems seminar**Title:**Special representations of group actions and low complexity tilings of groups**Speaker:**Ayse Sahin, DePaul University**Location:**MB114Generalizing a result of Alpern, Rudolph showed that the orbits of any measurable, measure preserving R^d action can be measurably tiled by 2^d rectangles and asked if this number of tiles is optimal. In joint work with B. Kra and A. Quas, we show that d+1 tiles suffice. Furthermore, for flows with completely positive entropy, this bound is optimal.

- February 11th, 2014 (10:00am - 10:50am)
**Seminar:**Hyperbolic and Mixed Type PDEs Seminar**Title:**On compactness estimates for Hamilton-Jacobi equations**Speaker:**Khai T. Nguyen, Penn State University**Location:**MB216Consider a first-order Hamilton-Jacobi equation ut(t,x)+H(∇u(t,x))=0, x∈RN, t>0, (0.1) with a strictly convex and coercive Hamiltonian H : RN → R. For every u ∈ W 1,1(RN , R), let Stu =. u(t,·) denote the unique viscosity solution of (0.1) with initial data u(0,·) = u. Having in mind the analysis recently developed for solutions to conservation laws [2-4], inspired by a question posed by Lax, we are interested in studying the compactifying effect of the operator St, at any fixed time t > 0, w.r.t the W1,1-topology. Namely, we wish to estimate the Kolmogorov ε-entropy in W1,1 of the image of bounded sets of initial data through the map St. We recall that, given a metric space (X, d), and a totally bounded subset K of X, we let Nε(K | X) denote the minimal number of sets in a cover of K by subsets of X having diameter ≤ 2ε, and define the Kolmogorov ε-entropy of K as Hε(K | X) =. log2 Nε(K | X). Entropy numbers play a central roles in various areas of information theory and statistics as well as of ergodic and learning theory. In the present setting, as suggested by Lax, this concept could provide a measure of the order of “resolution” of a numerical method for (0.1). Our main result in [1] shows that, for every fixed L,M > 0, letting C[L,M] denote the set of Lipschitz functions u : RN → R with Lipschitz constant L and with support contained in [−M,M]N, there holds Hε ST (C[L,M ] ) | W 1,1 (RN , R) ≈ (1/εN ). (0.2) Relying on fine properties of monotone operators we derive upper estimates on the ε-entropy of classes of semiconcave functions, which in turn yield upper estimates on Hε(ST(C[L,M])). Instead, lower bounds on Hε(ST (C[L,M])) are established in two steps. We first introduce a class of semiconcave functions SF defined as combinations of suitable bump functions, and with a combinatorial argument we provide an optimal lower estimate on the ε-entropy of such a class. Next, we prove a controllability result showing that any element of SF can be obtained, at any given time T > 0, as the value u(t,·) of a viscosity solution of (0.1), with initial data in C[L,M]. (Joint work with Fabio Ancona and Piermarco Cannarsa). References 1. Ancona F., Cannarsa P., Nguyen K.T., Quantitative compactness estimates for Hamilton- Jacobi Equations, preprint (2013). 2. Ancona F., Glass O., Nguyen K.T., Lower compactness estimates for scalar balance laws, Comm. Pure Appl. Math. 65 (2012), no. 9, 1303-1329. 3. Ancona F., Glass O., Nguyen K.T., On compactness estimates for hyperbolic systems of conservation laws, preprint (2013). 4. De Lellis C., Golse F., A Quantitative Compactness Estimate for Scalar Conservation Laws, Comm. Pure Appl. Math. 58 (2005), no. 7, 989–998.

- February 11th, 2014 (01:00pm - 02:00pm)
**Seminar:**Special Colloquium**Title:**Clearing and (functionally) curing HIV infection**Speaker:**Jessica Conway, Los Alamos National Laboratory**Location:**MB114I will discuss two models of within-host HIV viral dynamics (1) Analysis of a viral sample taken from any HIV positive individual reveals that 99.9-99.99% of circulating virus is non-infectious. Non-infectious virus may arise from errors at different steps in viral replication as well as other processes; the mechanism by which a virus becomes non-infectious does not affect predictions made with deterministic (ODE) models. However, during the earliest stages of HIV infection - between exposure and detectable infection - viral loads are small and are more appropriately modeled using a stochastic approach. In a stochastic version of a within-host model, the different types of errors generating defective virus will give different clinically relevant predictions, for example in risk of infection. We model within-host viral dynamics using continuous-time branching processes to investigate how viral replication error assumptions change predictions on risk of infection and time to infection clearance/detection. (2) Antiretroviral therapy (ART) for HIV increases both length and quality of life in HIV+ individuals, but is not a cure. However, a recent report from the VISCONTI study suggests that ART, initiated during primary infection, may induce post-treatment control (PTC) of HIV infection, i.e, HIV RNA < 50 copies/ml, after treatment termination. Our investigation explores the hypothesis that ART initiated during primary infection permits PTC by limiting the size of the latent reservoir, which if small enough at treatment termination, may allow the adaptive immune response to prevent viral rebound and control infection. We model within host HIV dynamics using differential equations to capture interactions between target cells, HIV-infected cells, latently HIV-infected cells, virus, and adaptive immune responses. Analysis of our model reveals a range in adaptive immune response strengths where a patient may either show viral rebound or PTC (bistability). Our model predicts that in this regime of bistability, there is a threshold in latent reservoir sizes at treatment termination below which PTC can be achieved. Using data on latent reservoir sizes in patients treated during primary infection, we also predict population-level viral rebound times for non-controllers consistent with observations in the VISCONTI study.

- February 11th, 2014 (02:30pm - 03:30pm)
**Seminar:**GAP Seminar**Title:**A Differential Graded Approach to Derived Manifolds**Speaker:**David Carchedi, Max Planck Bonn and Berkeley**Location:**MB106Given two smooth maps of manifolds $f:M \to L$ and $g:N \to L,$ if they are not transverse, the fibered product $M \times_L N$ may not exist, or may not have the expected dimension. In the world of derived manifolds, such a fibered product always exists as a smooth object, regardless of transversality. In fact, every (quasi-smooth) derived manifold is locally of this form. In this talk, we briefly explain what derived manifolds ought to be, why one should care about them, and how one can describe them. We end by explaining a bit of our joint work with Dmitry Roytenberg in which we make rigorous some ideas of Kontsevich to give a simple model for derived intersections as certain differential graded manifolds. Time permitting, we will compute some examples.

- February 11th, 2014 (02:30pm - 03:45pm)
**Seminar:**Logic Seminar**Title:**On the computability of rates of metastable convergence**Speaker:**Jason Rute, Penn State**Location:**MB315There are many ways to express that a sequence converges. They range from the most explicit but least uniform---a rate of convergence; to the moderately explicit and moderately uniform---a bound on the number of jumps by epsilon; to the least explicit but most uniform---a bound of metastable convergence (which I will define in this talk). Using proof theory, Kolhenbach showed that (under certain conditions) uniform metastable bounds can be computably extracted from the proof of a convergence theorem. Using model theory, Avigad and Iovino showed that (under similar conditions) metastable bounds of a convergence theorem are always uniform---but their methods do not provide a way to compute the bounds. Using computable analysis and computable model theory, I show that not only are the bounds always uniform, but they can computed from the statement of the theorem alone (without regards to the proof).

- February 11th, 2014 (03:30pm - 06:00pm)
**Seminar:**Working Seminar: Dynamics and its Working Tools**Title:**Anosov flows on 3-manifolds, III.**Speaker:**Thomas Barthelme, Penn State**Location:**MB216- February 11th, 2014 (03:50pm - 04:50pm)
**Seminar:**Tensor Networks and Applications Seminar**Title:**Boltzmann Machines**Speaker:**Jason Morton, Penn State University**Location:**MB315Abstract forthcoming.

- February 12th, 2014 (03:35pm - 04:35pm)
**Seminar:**Geometry Working Seminar**Title:**Educational talk: Metric on Lie groups, Riemannian submersions, O'Neil Formula, examples II**Speaker:**Dong Chen, PSU**Location:**MB114- February 12th, 2014 (03:45pm - 04:45pm)
**Seminar:**Complex Fluids Seminar**Title:**Spectral Methods for Spherical domain**Speaker:**Lina Ma, Purdue University**Location:**MB315- February 13th, 2014 (10:00am - 10:50am)
**Seminar:**Hyperbolic and Mixed Type PDEs Seminar**Title:**TBA**Speaker:**TBA**Location:**MB216- February 13th, 2014 (11:15am - 12:05pm)
**Seminar:**Algebra and Number Theory Seminar**Title:**Period functions for quantum modular forms**Speaker:**Trung Hieu Ngo, University of Michigan**Location:**MB106A quantum modular form is a function on the rational numbers which is not necessarily modular but whose failure to be modular gives rise to an interesting analytic function. There are two important places where one finds a quantum modular form. First, it arises from a certain transform of the period function of a Maass form (thanks to Ramanujan, Andrews, Dyson, Hickerson, Cohen, Bruggeman, Lewis, Zagier,...). Second, it arises from the radial limit of both a mock theta function and a partial theta function (thanks to Rademacher, Ramanujan, Rhoades, Zagier, Zwegers,...). It is a conjecture of Dyson that the two instances belong to a unified framework. With Yingkun Li and Robert C. Rhoades, we discover and study a q-hypergeometric series construction, called renormalization, which tie together a duality in each of the two instances. We will describe a new application of renormalization results and quantum modular forms to counting integer partitions with prescribed properties. This is achieved via certain circle method technique, executed by Hardy-Ramanujan and Wright amongst others. The talk includes a motivated introduction to quantum modular form (with more emphasis on the perspective of Bruggeman-Lewis-Zagier). No background knowledge is assumed and graduate students are welcome.

- February 13th, 2014 (11:30am - 01:00pm)
**Seminar:**Teaching Seminar**Title:**ALEKS Placement Testing: A panel discussion on its current usage as a mathematics diagnostics and remediation toolset.**Speaker:**James Sellers, Tanya Furman, Janet Schulenberg**Location:**MB114**Abstract:**http://- February 13th, 2014 (02:30pm - 03:30pm)
**Seminar:**Noncommutative Geometry Seminar**Title:**Braided noncommutative join construction**Speaker:**Piotr Hajac, Polish Academy of Sciences**Location:**MB106We construct the join of noncommutative Galois objects (quantum torsors) over a Hopf algebra H. To ensure that the join algebra enjoys the natural (diagonal) coaction of H, we braid the tensor product of the Galois objects. Then we show that this coaction is principal. Our examples are built from the noncommutative torus with the natural free action of the classical torus, and a certain finite-dimensional non-cosemisimple Hopf algebra thought of as a Galois object over itself. The former yields a noncommutative deformation of a non-trivial torus bundle, and the latter a finite quantum covering. (Joint work with L. Dabrowski, T. Hadfield and E. Wagner.)

- February 13th, 2014 (02:30pm - 03:20pm)
**Seminar:**PMASS Colloquium**Title:**Billiard table as mathematician's playground**Speaker:**Anatole Katok, Penn State**Location:**MB113Motion of an ideal particle ("a billiard ball") inside a bounded plane domain with the usual elastic reflection law `"the angle of incidence is equal to the angle of reflection'' is one of the simplest mechanical problems and attempts to describe this motion lead both to remarkable open problems and to connections with a variety of deep mathematical theories. For example, it is still not known whether inside any triangle there is a periodic billiard motion. It is also not known whether there is twice differentiable convex curve such that some billiard motion inside it is dense. In this talk I will give a very brief and elementary introduction to the beauty and complexity of this problem that looks so deceptively simple.

- February 13th, 2014 (03:35pm - 04:25pm)
**Seminar:**Department of Mathematics Colloquium**Title:**Evolution equations driven by nonlocal infinitesimal generators and their probabilistic interpretations**Speaker:**Wojbor Woyczynski, Case Western Reserve University**Location:**MB114One of the motivations of our program was to develop understanding of the interplay between the nonlinear and nonlocal components in evolution equation driven by the infinitesimal generators of stochastic processes with jumps, such as Levy processes and flights. In particular, we also studied probabilistic approximations (propagation of chaos) for several extensions of the classical quasilinear and strongly linear PDEs, including the conservation laws, porous medium and Hamilton-Jacobi equations, and reaction-diffusion type equations for Darwinian evolutionary population models where the hydrodynamic limits may still preserve some "background" random noise.

- February 13th, 2014 (04:00pm - 05:30pm)
**Seminar:**Complex Fluids Seminar**Title:**Introduction of the General Diffusion**Speaker:**Chun Liu, Penn State University**Location:**MB113**Abstract:**http://- February 14th, 2014 (12:00pm - 01:00pm)
**Seminar:**Mathematical Biology and Physiology Seminar**Title:**Optimal Within-Host Treatment and the Role of Resource Mediated Competitive Release**Speaker:**Elsa Hansen, CIDD, at Penn State**Location:**MB114Experimental results show that treatment can actually accelerate the growth of resistant pathogens via the mechanism of competitive release. It is unknown how treatment should be administered in order to mediate this effect while maintaining health gains. I will discuss an ongoing project where I am applying Pontryagin's Maximum Principle to a within-host model of disease spread to determine how competitive release can modulate the shape of the optimal treatment strategy. I will begin with a brief review of Pontryagin's Maximum Principle and then discuss my progress to date.

- February 14th, 2014 (12:20pm - 01:10pm)
**Seminar:**Teaching Mathematics Discussion Group Seminar**Title:**Teaching Study Strategies**Speaker:**Attendees, Penn State**Location:**MB101This week, we will discuss teaching study strategies to students. There can be very useful, but also time consuming. The discussion will be centered around the paper whose title and abstract are listed below. Incorporating Study Strategies in Developmental Mathematics/College Algebra The purpose of this paper is to discuss the effectiveness of incorporating study strategies in a developmental mathematics/college algebra program. Both quantitative and qualitative data were collected through a quasiexperimental methodology. Results show that students reported increases on the Learning and Study Strategies Inventory (LASSI) scales in study strategy usage, and this new strategy usage was supported by comments students made on open-ended surveys. A discussion of conclusions, limitations, recommendations, and suggestions is also included. A copy of the paper can be found in the site below. Copies of the paper will be available at the meeting. http://eric.ed.gov/?id=EJ986274

- February 14th, 2014 (03:30pm - 05:00pm)
**Seminar:**CCMA PDEs and Numerical Methods Seminar Series**Title:**Phase Field Modeling of Electrodeposition in Electrochemical systems and its application Li Dendrite Formation in Li-ion Batteries**Speaker:**Lei Chen, Department of Materials Science and Engineering, PSU**Location:**MB315We have developed a nonlinear phase-field model of electrodepostion in electrochemical systems. The main thermodynamic driving forces for the electrode-electrolyte interface evolution are limited to local variations of overpotential and chemical potential. Its application to the half-cell of lithium ion batteries explicitly describes ions diffusion in the electrolyte, cations deposition on the electrode surface and an electrochemical reaction at the electrode-electrolyte interface during charging operations. The lithium electrodeposition rate exactly follows the classical Butler-Volmer kinetic with exponentially and linearly depending on local variations of overpotential and cation concentration at the electrode surface, respectively. Simulation results show that the growth of dendritic deposit in electrochemical systems is well captured by the proposed diffuse-interface model. The longer and thicker deposits are observed both for larger charged current densities and reaction rate constants where the surface reaction rate is high.

- February 17th, 2014 (12:20pm - 01:30pm)
**Seminar:**CCMA Luncheon Seminar**Title:**Diffusion Maps for data-driven dimensionality reduction**Speaker:**Tyrus Berry, Penn State University**Location:**MB114Diffusion Maps is an algorithm for finding and describing low-dimensional structure in high-dimensional data based on concepts from Riemannian geometry. Diffusion Maps relies on a geometric prior which assumes that the data set lies `near' a low-dimensional smooth manifold embedded in a high-dimensional Euclidean space. A theoretical result of Coifman and Lafon shows that, using only the data and with no other prior information about the manifold structure, the Diffusion Maps construction converges to the Laplace-Beltrami operator on the manifold in the limit of large data. Since the Laplace-Beltrami operator determines the Riemannian metric, the Diffusion Maps algorithm captures all aspects of the geometry in the limit of large data. In this talk I give a comprehensive overview of Diffusion Maps including an explanation of the algorithm along with visualizations and explanations of the intuition behind the steps. I will also review the key theoretical results and some applications as time permits.

- February 17th, 2014 (02:30pm - 03:30pm)
**Seminar:**Computational and Applied Mathematics Colloquium**Title:**Diffusion Mapped Delay Coordinates (DMDC) and the geometry of dynamical data**Speaker:**Tyrus Berry, Penn State University**Location:**MB106In this talk I will examine the geometry of attractor reconstruction and show how the induced geometry of time-delay coordinates increasingly biases the reconstruction toward the stable directions as delays are added. This bias can be exploited, using the diffusion maps approach to dimension reduction, to extract dynamics on desired time scales from high-dimensional observed data. I discuss the technique of Diffusion Mapped Delay Coordinates (DMDC) and its application to video data from experiments. Time permitting I will introduce Local Kernels as a generalization of the isotropic kernels used in Diffusion Maps which can access geometries other than the induced geometry.

- February 17th, 2014 (03:35pm - 05:35pm)
**Seminar:**Dynamical systems seminar**Title:**Kakutani equivalence and restricted orbit equivalence in ergodic theory and dynamics, I: Introduction and overview, Part 1. This is WORKING SEMINAR; DYNAMICS AND ITS WORKING TOOLS talk**Speaker:**Anatole Katok, Penn State**Location:**MB114- February 17th, 2014 (08:00pm - 09:00pm)
**Seminar:**Chemerda Lectures**Title:**The maggot in the apple: peaceful coexistence of incompatible theories**Speaker:**Michael Berry, H H Wills Physics Laboratory, University of Bristol, UK**Location:**MB114In physics, as in science generally, most phenomena can be understood in more than one way: the gas in an engine obeys the laws of thermodynamics and also those of the motion of its molecules. The different theories correspond to different levels of description. These must overlap, but understanding their consilience is far from straightforward because they are usually based on seemingly incompatible concepts. The discordance arises from the fact, unappreciated until recently, that the limit in which the more general theory reduces to the less general (older) theory is mathematically singular. One consequence is a range of phenomena, of intense current interest, inhabiting the borderlands between the theories. I will explore this theme with examples from the physics of fluids, light and the quantum world.

- February 18th, 2014 (02:30pm - 03:45pm)
**Seminar:**Logic Seminar**Title:**NO SEMINAR THIS WEEK**Speaker:**NO SEMINAR THIS WEEK**Location:**MB315- February 18th, 2014 (03:30pm - 06:00pm)
**Seminar:**Working Seminar: Dynamics and its Working Tools**Title:**Kakutani equivalence and restricted orbit equivalence in ergodic theory and dynamics, I: Introduction and overview, Part 2 ATTENTION: This talk will start at 4:40 to avoid conflict with Chemerda Lectures**Speaker:**Anatole Katok, Penn State**Location:**MB216- February 18th, 2014 (03:35pm - 04:35pm)
**Seminar:**Chemerda Lectures**Title:**Superoscillations and weak measurement**Speaker:**Michael Berry, H H Wills Physics Laboratory, University of Bristol, UK**Location:**MB114Band-limited functions can oscillate arbitrarily faster than their fastest Fourier component over arbitrarily long intervals. Where such ‘superoscillations’occur, functions are exponentially weak. In typical monochromatic optical fields, substantial fractions of the domain (one-third in two dimensions) are superoscillatory. Superoscillations have implications for signal processing, and raise the possibility of sub-wavelength resolution microscopy without evanescent waves. In quantum mechanics, superoscillations correspond to weak measurements, suggesting ‘weak values’ of observables (e.g photon momenta) far outside the range represented in the quantum state. A weak measurement of neutrino speed could lead to a superluminal result without violating causality, but the effect is too small to explain the speed claimed in a recent (now discredited) experminent.

- February 18th, 2014 (03:50pm - 04:50pm)
**Seminar:**Tensor Networks and Applications Seminar**Title:**Algorithms for Simulating Hamiltonians**Speaker:**Nai-Hui Chia, Penn State University**Location:**MB315Simulating the dynamics of quantum systems is one of the most important (and the earliest) motivation for studying quantum computer. Given the Hamiltonian of a system and a particular time, the problem is to obtain the state of the system after the time interval. For Hamiltonian which can be approximated by a sum of local Hamiltonians, we can obtain the state by Trotter formular. The idea is to decompose the system into several small subsystems to calculate the dynamics for each, and then merge them together. Finally, in order to approximate the true state within certain error bound, we repeat the process many times. Note the efficiency of the process depends on the number and the simulating hardness of local Hamiltonians, it is interesting to figure out in which form Hamiltonians can be efficiently simulated. In this talk, I will introduce algorithms for simulating sparse Hamiltonians (where each row only has logarithmic number of non-zero entries) and some non-sparse Hamiltonians (including density matrices and matrices in particular form.)

- February 19th, 2014 (12:05pm - 01:20pm)
**Seminar:**Geometry Luncheon Seminar**Title:**A Paneitz-type operator for CR pluriharmonic functions**Speaker:**Jeffrey Case, Princeton University**Location:**MB114Abstract: We introduce a fourth order CR invariant operator on pluriharmonic functions on a three-dimensional CR manifold, generalizing to the abstract setting the operator discovered by Branson, Fontana and Morpurgo. For a distinguished class of contact forms, all of which have vanishing Hirachi-$Q$ curvature, these operators determine a new scalar invariant with properties analogous to the usual $Q$-curvature. We discuss how these are similar to the (conformal) Paneitz operator and $Q$-curvature of a four-manifold, and describe its relation to some problems for three-dimensional CR manifolds. This is joint work with Paul Yang.

- February 19th, 2014 (03:35pm - 04:35pm)
**Seminar:**Chemerda Lectures**Title:**Curl forces**Speaker:**Michael Berry, H H Wills Physics Laboratory, University of Bristol, UK**Location:**MB114Forces depending on position but which are not derivable from a potential, that is, forces with non-zero curl, give rise to dynamics that is not Hamiltonian or Lagrangian, while also being non-dissipative. Noether’s theorem does not apply, so the link between symmetries and conservation laws is broken. The physical existence of curl forces has been controversial and the subject of intense debate among engineers. But an example is familiar in optics: force on a dielectric particle in an optical field. Motion under curl forces near optical vortices can be understood in detail; understanding these forces beyond the adiabatic regime involves the geometric phase 2-form and slow manifold theory.

- February 20th, 2014 (10:00am - 10:50am)
**Seminar:**Hyperbolic and Mixed Type PDEs Seminar**Title:**Mixed type boundary value problems**Speaker:**Joe Roberts, Penn State University**Location:**MB216I will discuss some mixed type boundary value problems relevant to the study of the two-dimensional steady Euler equations. I will present some existence and uniqueness results for linear problems, and explain how certain solvability conditions do not hold for perturbation problems for transonic flows with a local supersonic region in a channel. Therefore the solutions to the linearized equations must have singularities, corresponding to shocks in the nonlinear equations. These topics are from Chapters 1 and 3 of \emph{Boundary Value Problems for Transonic Flow} by A. G. Kuz'min.

- February 20th, 2014 (11:15am - 12:05pm)
**Seminar:**Algebra and Number Theory Seminar**Title:**Expanders and Ramanujan complexes**Speaker:**Ori Parzanchevski, IAS**Location:**MB106The "Ramanujan graphs" constructed by Lubotzky-Phillips-Sarnak and Margulis are sparse graphs with excellent expansion properties. Their higher dimensional analogues are "Ramanujan complexes", which are at the focus of several recent studies. In joint work with Konstantin Golubev we study the simplicial Hodge spectrum of these complexes, and derive some combinatorial expansion properties.

- February 20th, 2014 (03:35pm - 04:25pm)
**Seminar:**Department of Mathematics Colloquium**Title:**Sharp Gagliardo--Nirenberg--Sobolev inequalities and conformal geometry**Speaker:**Jeffrey Case, Princeton University**Location:**MB114There is a deep connection between curvature prescription problems in conformal geometry and sharp Sobolev inequalities. One famous example is the connection between prescribing conformal metrics with constant scalar curvature and the sharp $L^2$ Sobolev inequalty. Another example is the connection between prescribing Perelman's weighted scalar curvature and the sharp logarithmic Sobolev inequality. In this talk, I will describe an interpolating family of curvature prescription problems on smooth metric measure spaces which connect the scalar curvature to Perelman's weighted scalar curvature and are related to the family of sharp Gagliardo-Nirenberg-Sobolev inequalities discovered by Del Pino and Dolbeault. In particular, this provides a new perspective on Perelman's $W$-functional and suggests an approach to finding higher order analogues.

- February 21st, 2014 (12:00pm - 01:00pm)
**Seminar:**Mathematical Biology and Physiology Seminar**Title:**Cell Polarization in Budding Yeast**Speaker:**Ching-Shan Chou, Department of Mathematics, Ohio State University**Location:**MB114Cell polarization, in which intracellular substances localize to a particular spot in response to external stimuli or internal cues, is central to cell physiology, and it underlies processes such as cell motility, cell division and cell differentiation. In this talk, I will present our recent works, using budding yeast as a model system, on how cells initiate symmetry breaking preceding the new bud emergence or mating projection. Along with experimental data, our mathematical modeling and simulations reveal potential mechanisms which underlie a biased cell polarity and pheromone concentration dependent cell morphology.

- February 21st, 2014 (12:20pm - 01:10pm)
**Seminar:**Teaching Mathematics Discussion Group Seminar**Title:**Theories of Intelligence**Speaker:**Attendees, Penn State**Location:**MB101We will discuss, "Longitudinal changes in college math students’ implicit theories of intelligence." This study examined changes over time in implicit theories of intelligence and their relationships to help-seeking and academic performance. College algebra students completed questionnaires during the second week of classes and 2 weeks before the end of the semester (ns = 159 and 145, respectively; 61 students completed questionnaires at both waves). The questionnaires assessed entity and incremental implicit theories of general and math intelligence (beginning and end of semester) and help-seeking (end of semester). Results indicated that students had more incremental views of general than math intelligence. Further, their views became less incremental over the course of the semester; however, this decrease was greater for math than for general intelligence. Participants who exhibited a stronger incremental theory of general intelligence at the beginning of the semester subsequently reported greater help-seeking during the semester. Finally, students who had more entitative views of math intelligence earned lower course grades. The paper can be found at the link below. Copies will be provided at the meeting. http://link.springer.com/article/10.1007%2Fs11218-012-9208-0#

- February 21st, 2014 (03:30pm - 05:00pm)
**Seminar:**CCMA PDEs and Numerical Methods Seminar Series**Title:**W-cycle algorithms for hp-Discontinuous Galerkin discretizations**Speaker:**Marco Sarti, Politecnico di Milano**Location:**MB315In this talk I will discuss the main issues regarding the application of multigrid algorithms to high order Discontinuous Galerkin discretizations. I will first briefly introduce several Discontinuous Galerkin schemes for the Poisson equation, recalling some standard results regarding the well posedness of the problem and the error estimates. Then I will analyze the multilevel framework and underline the main differences with the conforming case. I will show that, employing standard smoothing schemes, we can recover the well known uniformity of the rate of convergence with respect to the mesh size and the number of levels, but the dependence on the polyonomial order employed cannot be eliminated. The theoretical estimates are then supported by several numerical tests on two and three dimensional model problems.

- February 21st, 2014 (03:35pm - 04:35pm)
**Seminar:**Probability and Financial Mathematics Seminar**Title:**Anomalous Diffusion in Cellular Flows**Speaker:**Alexei Novikov, Penn State**Location:**MB106This is basically continuation of my talk 3 weeks ago. I consider a passive scalar in a periodic cellular flow perturbed by an additive Brownian Motion. It is well-known a long time/large distance homogenization limit is diffusive: long-time mean-square displacement is proportional to time. I show that mean-square displacement is proportional to square root of time for intermediate times.

- February 24th, 2014 (12:20pm - 01:30pm)
**Seminar:**CCMA Luncheon Seminar**Title:**Discretization of PDEs on evolving interfaces**Speaker:**Arnold Reusken, INSTITUT FÜR GEOMETRIE UND PRAKTISCHE MATHEMATIK**Location:**MB114**Abstract:**http://www.igpm.rwth-aachen.de/personen/reuskenWe consider a ow problem with two dierent immiscible incompressible newto- nian phases ( uid- uid or uid-gas). In many applications so-called surfactants play an important role. These attach to the interface and are transported, due to diusion and convection, on the evolving interface. This surfactant trans- port can be modeled by a convection-diusion equation on the surface. In this talk we present a nite element method for the discretization of the surfactant equation on the evolving interface.

- February 24th, 2014 (02:30pm - 03:30pm)
**Seminar:**Computational and Applied Mathematics Colloquium**Title:**Finite element methods for incompressible ows with moving interfaces**Speaker:**Arnold Reusken, INSTITUT FÜR GEOMETRIE UND PRAKTISCHE MATHEMATIK**Location:**MB106**Abstract:**http://www.igpm.rwth-aachen.de/personen/reuskenWe consider a ow problem with two dierent immiscible incompressible new- tonian phases ( uid- uid or uid-gas). A standard model for this consists of the Navier-Stokes equations with a viscosity and density that are discontinuous across the interface and with a localized force at the interface that describes surface tension eects. This uid dynamics model can be coupled with a model for mass transport between the phases and a model for transport of surfac- tants on the interface. We discuss why the ecient and accurate numerical simulation of such models is a very challenging problem. Two topics, namely the discretization of the mass transport equation and the discretization of the surfactant equation on the evolving interface will be treated in more detail.

- February 24th, 2014 (03:30pm - 04:30pm)
**Seminar:**Complex Fluids Seminar**Title:**On stability of geophysical fluid systems and the Navier-Stokes-Boussinesq type system**Speaker:**Hajime Koba, Waseda University**Location:**MB315**Abstract:**http://- February 24th, 2014 (03:35pm - 05:35pm)
**Seminar:**Dynamical systems seminar**Title:**Kakutani equivalence and restricted orbit equivalence in ergodic theory and dynamics, II: Actions of higher rank abelian groups and new rigidity problems. This is WORKING SEMINAR; DYNAMICS AND ITS WORKING TOOLS talk**Speaker:**Anatole Katok, Penn State**Location:**MB114- February 25th, 2014 (10:00am - 10:50am)
**Seminar:**Hyperbolic and Mixed Type PDEs Seminar**Title:**Global solutions for the Burgers-Hilbert equation**Speaker:**Alberto Bressan, Penn State University**Location:**MB216The Burgers-Hilbert equation has been derived by J.Biello and J.Hunter as a model for nonlinear waves with constant frequency. This talk will present some recent results (in collaboration with Khai Nguyen). Namely: the global existence of entropy weak solutions, a priori estimates in L^2 and in L^\infty, and a uniqueness result in the spatially periodic case. Open questions, concerning the uniqueness and stability of solutions, and the onset of singularities, will be discussed.

- February 25th, 2014 (12:06pm - 02:06pm)
**Seminar:**Ph.D. Oral Comprehensive Examination**Title:**"Fibrations of Euclidean Space by Skew Flat Fibers"**Speaker:**Mike Harrison, Adviser: Sergei Tabachnikov/Kris Wysocki, Penn State**Location:**MB106**Abstract:**http://Two copies of R^p are called skew if they neither intersect nor contain parallel directions. We discuss a recent result of Ovsienko and Tabachnikov which gives conditions on p and n for the existence of a fibration of R^n by pairwise skew, oriented copies of R^p. We then provide some positive results in the direction of classifying skew fibrations, including a slight generalization of Salvai's recent characterization of smooth, skew fibrations in the case where n=3 and p=1. To conclude, we examine the relationship between spherical fibrations and flat fibrations, and we offer a number of avenues for further study in this area.

- February 25th, 2014 (02:30pm - 03:30pm)
**Seminar:**GAP Seminar**Title:**Exponential map and L-infinity algebra associated to a Lie pair**Speaker:**Mathieu Stienon, Penn State**Location:**MB106In this talk, we unveil homotopy-rich algebraic structures generated by the Atiyah classes relative to a Lie pair $(L,A)$ of algebroids. In particular, we prove that the quotient $L/A$ of such a pair admits an essentially canonical homotopy module structure over the Lie algebroid $A$, which we call Kapranov module.

- February 25th, 2014 (02:30pm - 03:45pm)
**Seminar:**Logic Seminar**Title:**Invariant measures on homogeneous structures**Speaker:**Jan Reimann, Penn State**Location:**MB315Many constructions of universal homogeneous structures can be randomized. The most famous example is arguably the Rado graph, which can obtained by chosing edges randomly with probability 0 < p < 1. Other examples include the universal K_n-free graph (Petrov and Vershik), and the Urysohn space (Vershik). The existence of such a randomized construction is closely tied to the existence of a measure on the homogeneous structure that is invariant under the logic action. In this talk I will survey a number of important results on such measures.

- February 25th, 2014 (04:00pm - 05:00pm)
**Seminar:**Applied Analysis Seminar**Title:**Logarithmic interaction energy for infinitely many points in the plane**Speaker:**Etienne Sandier, Université Paris 12, Paris, France**Location:**MB106I will define an energy describing the interaction of infinitely many positive charges in the plane with a uniform negative background (a system sometimes referred to as a jellium by physicists). I will give some of the basic properties of this energy proved with S. Serfaty some years ago, and describe recent results obtained with Y.Ge which give a partial answer to the question of which configurations of points have finite energy. I will also if time permits describe links and applications to the theory of log-gases and weighted Fekete sets.

- February 25th, 2014 (04:00pm - 05:00pm)
**Seminar:**Computational and Applied Mathematics Colloquium**Title:**Finite volume methods for elasticity and poro-elasticity**Speaker:**Jan Martin Nordbotten, University of Bergen**Location:**MB114**Abstract:**http://folk.uib.no/nmajn/index-eng.htmlWe introduce a new class of cell-centered finite volume methods for elasticity and poro-elasticity. This class of discretization methods has the advantage that the mechanical discretization is fully compatible (in terms of grid and variables) to the standard cell-centered finite volume discretizations that are prevailing for commercial simulation of multi-phase flows in porous media. For a specific variant of the proposed discretization, we give an overview of a convergence proof in the setting of isotropic elasticity, and address from a theoretical perspective the issues of a discrete Korn's inequality and robustness with respect to locking. Furthermore, we give numerical results for both structured and unstructured grids for both elasticity and poro-elasticity. The talk concludes with an application to simulation of fractured and fracturing porous media.

- February 26th, 2014 (03:35pm - 04:35pm)
**Seminar:**Geometry Working Seminar**Title:**Working Seminar**Speaker:**Dong Chen, Jinpeng Lu, PSU**Location:**MB114Dong will continue on structures on homogeneous spaces (thanks!), on John Milnor classic result that got a Fields medal, Then Jinpeng Lu is going to continue on a classic injectivity radius estimate by Klingenberg.

- February 27th, 2014 (10:00am - 10:50am)
**Seminar:**Hyperbolic and Mixed Type PDEs Seminar**Title:**Mixed type boundary problems continued**Speaker:**Joe Roberts, Penn State**Location:**MB216- February 27th, 2014 (11:15am - 12:05pm)
**Seminar:**Algebra and Number Theory Seminar**Title:**Invariants of Local Conjugation**Speaker:**Jacob Turner, PSU**Location:**MB106We consider the action of a product of groups acting on tuples of matrices by simultaneous conjugation. We focus on the case where the groups are products of (special) unitary or (special) linear groups. We classify the invariant rings and for a special case, we give an upper bound on the degree of the generators.

- February 27th, 2014 (02:30pm - 03:20pm)
**Seminar:**PMASS Colloquium**Title:**Probability puzzles**Speaker:**Victoria Sadovskaya, Penn State**Location:**MB113We will discuss several problems in elementary probability where intuition may give a wrong answer while the correct one seems, at first glance, unlikely or even impossible.

- February 27th, 2014 (03:35pm - 04:25pm)
**Seminar:**Department of Mathematics Colloquium**Title:**The Atlas of Lie Groups and representations**Speaker:**Jeffrey Adams, University of Maryland**Location:**MB114One of the fundamental problems in the theory of Lie groups is to classify the Unitary Dual of a group G: the irreducible representations of G, acting on a (typically infinite dimensional) Hilbert space, preserving the inner product. This is a very difficult problem, unsolved except in some special cases, and the answer is known to be very complicated. The primary goal of the Atlas project is to compute the Unitary Dual by computer, even though it is not obvious there is a finite algorithm in principle, not to mention in practice. An important auxiliary goal is to provide software for doing computations in Lie theory and representation theory. I'll discuss the current state of the project, in broad terms, and talk about what we've learned by rethinking our entire subject in computational terms.

- February 28th, 2014 (12:00pm - 01:00pm)
**Seminar:**Mathematical Biology and Physiology Seminar**Title:**Street fighters - Territorial scaling in ant battles**Speaker:**Fred Adler, Department of Mathematics, University of Utah**Location:**MB114The pavement ant Tetramorium caespitum wages huge battles on sidewalks, apparently to establish territorial foraging boundaries for the season. We used empirical data to create a model of where these boundaries will develop as a function of the recruitment strategies of the ants. Larger colonies gain disproportionately large territories, leading to a scaling relationship of colony size with territory size with a slope that can be estimated analytically and which depends in counterintuitive ways on ecological conditions and the strength of recruitment.

- February 28th, 2014 (03:35pm - 04:35pm)
**Seminar:**Probability and Financial Mathematics Seminar**Title:**On C^1 diffeomorphisms, homoclinic classes and hyperbolic properties**Speaker:**Welington Cordeiro, Fderal University of Rio de Janeiro**Location:**MB106The study of homoclinc classes for more general dynamics attracts a lot of attention by many researches. Indeed, it is an important problem to decide if such classes are hyperbolic under certain dynamical assumptions. Actually, there are many satisfactory results about generic tame diffeomorphisms, where all homoclinic classes are isolated. It is natural to study the complementary class, the so called wild diffeomorphisms. In particular, to study non-isolated homoclinic classes. We will discuss properties as expansiveness, shadowing, specification and limit shadowing in homoclinic classes of C^1 generic diffeomorphisms seeking conditions for these classes to be isolated or hyperbolic.