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- October 1st, 2014 (12:05pm - 01:20pm)
**Seminar:**Geometry Luncheon Seminar**Title:**Chain theorems with period six**Speaker:**Arseniy Akopyan, IITP Russ. Acad. Sci, visiting PSU.**Location:**MB114The Poncelet and Steiner theorems are probably the most famous chain theorems. In my talk I will demonstrate a class of similar theorems which are usually related with a triangle and have period 6.

- October 1st, 2014 (02:30pm - 03:20pm)
**Seminar:**Applied Algebra and Network Theory Seminar**Title:**Permutohedral Arrangements, Simplicial Decompositions and a Geometrization of the Classical Worpitzky Identity**Speaker:**Nick Early, Penn State**Location:**MB106In forthcoming joint work with Adrian Ocneanu, we prove a symmetric group character formula conjectured several years ago by the latter as he was studying certain polyhedra emerging from hyperplane arrangements in simplices. We reveal the geometric content which lies behind the classical Worpitzky identity, which expands a cubical number $r^{n-1}$ in terms of the Eulerian numbers. Our proof suggests a new geometric interpretation of combinatorial results of Sagan-Shareshian-Wachs on Eulerian quasi-symmetric functions.

- October 1st, 2014 (03:30pm - 05:00pm)
**Seminar:**Complex Fluids Seminar**Title:**Some problems on the two-phase flows with diffuse interface-part II**Speaker:**Yinghua Li, South China Normal University**Location:**MB106We consider the well-posedness of 1-D compressible Navier-Stokes/Cahn-Hilliard system, 1-D compressible Navier-Stokes/Allen-Cahn system, and the blow-up criterion of incompressible Navier-Stokes/Allen Cahn system with different densities in 2-D and 3-D.

- October 1st, 2014 (03:35pm - 04:25pm)
**Seminar:**Teaching Mathematics Discussion Group Seminar**Title:**How Mathematicians Gain Conviction**Speaker:**Attendees, Penn State**Location:**MB102Mathematics is often thought of as a discipline that gains certainty by deductive reasoning rather than empirical or authoritarian evidence. In practice, however, this may not be entirely true. This week, we read a paper on this very topic and discuss if we teach the practice of mathematics honestly.

Weber, K., Inglis, M., & Mejia-Ramos, J. P. (2014). How mathematicians obtain conviction: Implications for mathematics instruction and research on epistemic cognition.*Educational Psychologist,*49(1), 36-58.- October 2nd, 2014 (10:00am - 10:50am)
**Seminar:**Hyperbolic and Mixed Type PDEs Seminar**Title:**Set-up of a mixed type problem for the pressure gradient system**Speaker:**Yuxi Zheng, Penn State**Location:**MB216We will collect relevant information around the edge of the hyperbolic region to form the free boundary and data for the interior elliptic domain.

- October 2nd, 2014 (11:15am - 12:05pm)
**Seminar:**Algebra and Number Theory Seminar**Title:**A reciprocity law for Drinfeld modules**Speaker:**Mihran Papikian, Penn State University**Location:**MB106First, I will explain what is a "reciprocity law". Then I will describe such law arising from Drinfeld modules. Finally, I will apply this law to derive a criterion for the splitting modulo primes of a class of non-solvable polynomials over $\mathbb{F}_q(T)$ that was studied by Abhyankar. (This is a joint work with Alina Cojocaru.)

- October 2nd, 2014 (01:25pm - 02:25pm)
**Seminar:**MASS Colloquium**Title:**Stimulus space geometry and topology from neural activity**Speaker:**Carina Curto, Penn State University**Location:**MB114Neural activity data can be used to infer subsets of co-active neurons in a network. By considering neurons in the hippocampus that encode position information, I will show how these data can be used to infer topological and geometric features of the stimulus space the neurons are encoding. Our results rely on an unexpected application of the Nerve Lemma from algebraic topology.

- October 2nd, 2014 (03:30pm - 04:20pm)
**Seminar:**Department of Mathematics Colloquium**Title:**Modeling Electrodiffusion and Osmosis in Physiological Systems**Speaker:**Yoichiro Mori, University of Minnesota (Host: Chun Liu)**Location:**MB114Electrolyte and cell volume regulation is essential in physiological systems. After a brief introduction to cell volume control and electrophysiology, I will discuss the classical pump-leak model of electrolyte and cell volume control. I will then generalize this to a PDE model that allows for the modeling of tissue-level electrodiffusive, convective and osmotic phenomena. This model will then be applied to the study of cortical spreading depression.

- October 3rd, 2014 (03:35pm - 04:35pm)
**Seminar:**Probability and Financial Mathematics Seminar**Title:**Ergodicity of avalanche transformations**Speaker:**Manfred Denker, PSU**Location:**MB106An avalanche transformation is a product transformation followed by an avalanche dynamics. The talk will provide a precise definition. I will discuss the question when such a transformation is ergodic, besides other questions like topological transitivity and central limit theorems.

- October 4th, 2014 (08:00am - 06:00pm)
**Seminar:**GAP Seminar**Title:**Joint Cornell-Penn State Symplectic Geometry Seminar**Speaker:**Various Speakers, Various Affiliations**Location:**MB114**Abstract:**http://www.math.psu.edu/stienon/cornellpennstate/schedule_FA14.pdfYuri Berest (Cornell University), David Li-Bland (University of California, Berkeley), Sasha Patotski (Cornell University), Nick Early (Penn State University), and Jae-Suk Park (Center for Geometry and Physics, IBS & POSTECH) See link for schedule.

- October 6th, 2014 (12:20pm - 01:30pm)
**Seminar:**CCMA Luncheon Seminar**Title:**Data driven methods for dynamical systems: Extracting spatiotemporal patterns from high-dimensional time series**Speaker:**Dimitrios Giannakis, New York University (Host: J Harlim)**Location:**MB114Large-scale datasets generated by dynamical systems arise in many applications in science and engineering. A research topic of current interest in this area involves using data collected through observational networks or output by numerical models to extract the salient modes of variability from high-dimensional data, and create low-order models to forecast these modes. In this talk we discuss applied mathematics techniques to address this topic blending ideas from machine learning, harmonic analysis, and delay-coordinate embeddings of dynamical systems. We illustrate these techniques with applications to climate atmosphere ocean science.

- October 6th, 2014 (02:30pm - 03:30pm)
**Seminar:**Computational and Applied Mathematics Colloquium**Title:**Extracting and predicting spatiotemporal patterns from data with dynamics-adapted kernels**Speaker:**Dimitrios Giannakis, New York University (Host: J Harlim)**Location:**MB106Kernel methods provide an attractive way of extracting features from data by biasing their geometry in a controlled manner. In this talk, we discuss a family of kernels for dynamical systems featuring an explicit dependence on the dynamical vector field operating in the phase-space manifold, estimated empirically through finite differences of time-ordered data samples. The associated diffusion operator for data analysis is adapted to the dynamics in that it generates diffusions along the integral curves of the dynamical vector field. We present applications to toy dynamical systems and comprehensive climate models. We also discuss a technique for analog forecasting based on these kernels. In this empirical forecasting technique, kernels are used to create weighted ensembles of states (analogs) with high similarity to the initial data from a record of historical observations, and the future values of observables are predicted from the historical evolution of the ensemble.

- October 6th, 2014 (03:35pm - 04:35pm)
**Seminar:**Dynamical systems seminar**Title:**The Random Minkowski Theorem and Values of Polynomials at Lattice Points**Speaker:**Jayadev Athreya, University of Illinois at Urbana-Champaign**Location:**MB114Motivated by problems of unipotent flows on homogeneous spaces, in 2008 we (the speaker and G. Margulis) proved a "Random Minkowski" theorem on the probability a randomly chosen unimodular lattice mises a large subset of Euclidean space. In this talk, we give applications of this theorem to give error terms (for almost every quadratic form) in the Quantitative Oppenheim results of Eskin-Margulis-Mozes. This is joint work with G. Margulis.

- October 7th, 2014 (01:00pm - 01:50pm)
**Seminar:**Theoretical Biology Seminar**Title:**Composite likelihood ratio tests for detecting natural selection**Speaker:**Michael DeGiorgio, Penn State

(Host: Tim Reluga)**Location:**MB106The study of genetic variation is fundamental to population and evolutionary genetics, as it provides a basis for understanding differences among individuals, populations, and species. This talk will focus on the development of statistical approaches for identifying the adaptive processes that have shaped the current distribution of genetic variation in populations. Three main adaptive forces are positive, negative, and balancing selection. In the first half of the talk, I will discuss an extension to a method for detecting recent positive selection that can take into account the effects of long-term negative selection, both of which can yield similar patterns in the genome. In the second half, I will introduce the first set of likelihood-based methods to scan for signals of long-term balancing selection. Simulation results show that these methods for detecting balancing selection are robust to population demography and are the most powerful developed to date.

- October 7th, 2014 (02:30pm - 03:45pm)
**Seminar:**Logic Seminar**Title:**To be announced**Speaker:**Sankha Basu, Penn State**Location:**MB315- October 7th, 2014 (03:30pm - 06:00pm)
**Seminar:**Working Seminar: Dynamics and its Working Tools**Title:**Invariant distributions for dynamical systems,I (tentative)**Speaker:**Alejandro Kocsard, Fluminense Federal University, Brazil**Location:**MB216- October 7th, 2014 (05:45pm - 06:45pm)
**Seminar:**Teaching Seminar**Title:**Midsemester Evaluations and Interpreting SRTEs**Speaker:**Larkin Hood, Research Associate and Instructional Consultant at SITE**Location:**MB114- October 8th, 2014 (03:35pm - 04:25pm)
**Seminar:**Teaching Mathematics Discussion Group Seminar**Title:**How Mathematicians Use Examples To Understand Proofs**Speaker:**Attendees, Penn State**Location:**MB102Everyone knows mathematicians use examples to explore conjectures... except for many undergraduate students. This week, we read a paper that details how mathematicians use examples when exploring a conjecture and discuss its implications for undergraduate education.

Lockwood, Elise, Amy B. Ellis, and Eric Knuth. "Mathematicians’ example-related activity when proving conjectures."*16TH Annual Conference on Research in Undergraduate Mathematics Education 1*(n.d.): 16-30. Web. 20 Aug. 2014.- October 9th, 2014 (11:15am - 12:05pm)
**Seminar:**Algebra and Number Theory Seminar**Title:**A quick tour of discrepancy theory**Speaker:**William Chen, MacQuarie University**Location:**MB106The birth of geometric discrepancy theory is usually attributed to the fundamental work of Klaus Roth in 1954. The present scope of the subject is due in no small part to the many important results of Wolfgang Schmidt in the 1960s and 1970s. It is fair to say that every subsequent worker in the subject have been motivated and encouraged, directly or indirectly, by these two pioneers and their work. Lower bound results in discrepancy theory exhibit the limitations to just point distributions, whereas upper bound results lead to point distributions that are close to best possible under such limitations. In this expository talk, we shall discuss some of the main results obtained over the last 60 years, and introduce to the audience a number of lower and upper bound techniques. We shall also briefly discuss some open questions.

- October 10th, 2014 (02:30pm - 03:30pm)
**Seminar:**Computational and Applied Mathematics Colloquium**Title:**How do dispersed inertial particles modify turbulent flows ?**Speaker:**Said Elghobashi, University of California, Irvine (Host: J Xu)**Location:**MB114Turbulent flows laden with inertial particles are ubiquitous in nature (e.g. aerosols in clouds, and dust storms on Earth and Mars) and in industrial applications (e.g. liquid fuel and pulverized coal sprays in combustion chambers). Experimental and numerical studies of these flows are quite challenging due to the wide spectra of length- and time- scales of the dispersed particles in addition to the spectra of scales intrinsic to the carrier fluid turbulence. The two-way and and four-way nonlinear interactions between the dispersed particles and the turbulence result in complex multi-scale physical phenomena. The lecture focuses on the physical mechanisms of interactions between dispersed spherical particles and isotropic turbulence using Direct Numerical Simulation (DNS). Particles whose diameter is smaller than the Kolmogorov length scale are simulated as point particles. Larger particles with diameter of the order of Taylor microscale are fully resolved using the Immersed Boundary method.

- October 10th, 2014 (03:35pm - 04:35pm)
**Seminar:**Probability and Financial Mathematics Seminar**Title:**On infinitely divisible semimartingales**Speaker:**Jan Rosinski, University of Tennessee**Location:**MB106Semimartingales play a fundamental role in stochastic analysis and mathematical finance. Concerning the latter, the discounted asset price process must be a semimartingale in order to preclude arbitrage opportunities. The question whether a given process with long memory, possible jumps and/or heavy tails is a semimartingale is also of importance in stochastic modeling, where such processes are used as a driving random motion for stochastic differential equations. We consider this question in the context of infinitely divisible processes, which include fractional processes, moving averages, and Ornstein-Uhlenbeck processes driven by stable, multi-stable, and tempered stable L\'evy processes, and their mixtures. We show that the problem when any such process is a semimartingale can often be reduced to a path property, when a certain associated infinitely divisible process is of finite variation. This gives the key to fully characterize the semimartingale property for many processes of interest, including processes mentioned above. This talk is based on a joint work with Andreas Basse-O'Connor of Aarhus University.

- October 13th, 2014 (03:35pm - 04:35pm)
**Seminar:**Dynamical systems seminar**Title:**TBA**Speaker:**Mikhail Lyubich, SUNY Stony Brook**Location:**MB114- October 14th, 2014 (01:00pm - 01:50pm)
**Seminar:**Theoretical Biology Seminar**Title:**Modeling Actin Regulation in Cancer Metastasis**Speaker:**Nessy Tania, Smith College

(Host: Jessica Conway)**Location:**MB106Directed cell movement, chemotaxis, is a part of normal physiological processes such as wound healing, immune response and embryogenesis. However, this pathway can also be hijacked during tumor development, allowing cancer cells to metastasize. In this talk, I will discuss an ongoing collaborative work in modeling the regulation of actin cytoskeleton in mammary carcinoma motility. I will survey results from a temporal ODE model of the regulation of cofilin, an actin regulatory protein that is upregulated in invasive carcinoma. Second, I will present a spatio-temporal model of actin growth to look at the collective effects of two actin regulatory proteins. At the end, I will motivate our current effort in studying invadopodia, a dynamic actin-based structure that allows cancer cell to 'dig' through its surrounding environment. This work is done jointly with John Condeelis (Albert Einstein College of Medicine) and Leah Edelstein-Keshet (University of British Columbia).

- October 14th, 2014 (02:30pm - 03:45pm)
**Seminar:**Logic Seminar**Title:**To be announced**Speaker:**Manfred Denker, Penn State**Location:**MB315- October 14th, 2014 (02:30pm - 03:30pm)
**Seminar:**Center for Dynamics and Geometry Colloquium**Title:**TBA**Speaker:**Mikhail Lyubich, SUNY Stony Brook**Location:**MB114- October 14th, 2014 (03:30pm - 06:00pm)
**Seminar:**Working Seminar: Dynamics and its Working Tools**Title:**Invariant distributions for dynamical systems,II (tentative)**Speaker:**Alejandro Kocsard, Fluminense Federal University, Brazil**Location:**MB216- October 14th, 2014 (05:45pm - 06:45pm)
**Seminar:**Teaching Seminar**Title:**Student Motivation**Speaker:**Jackie Bortiatynski, Senior Lecturer and Director for Excellence in ECoS**Location:**MB114- October 15th, 2014 (03:35pm - 04:25pm)
**Seminar:**Teaching Mathematics Discussion Group Seminar**Title:**A Uniform Standard for Evaluating Proofs?**Speaker:**Attendees, Penn State**Location:**MB102Courses as basic as Calculus incorporate proofs. Is the mathematical community consistent in how it evaluates such basic proofs? This week, we read a paper that explores different standards used by mathematicians and discuss if there exists a uniform standard by which we judge proofs.

Inglis, M., Mejia-Ramos, J.P., Weber, K., & Alcock, L. (2013). On mathematicians' different standards when evaluating elementary proofs.*Topics in Cognitive Science*5(2), 270-282- October 16th, 2014 (01:25pm - 02:25pm)
**Seminar:**MASS Colloquium**Title:**Ramsey Theory and Dynamics**Speaker:**Vitaly Bergelson, Ohio State University**Location:**MB113**Abstract:**http://We will start the talk with formulating and discussing some of the classical results of Ramsey theory, a branch of combinatorics which studies the structure of mathematical objects that is preserved under partitions. Next, we will show that some of these results can be naturally viewed as dynamical questions about the recurrence in topological and/or volume preserving systems. We will conclude with the discussion of some of the recent developments and open problems.

- October 16th, 2014 (03:30pm - 04:20pm)
**Seminar:**Department of Mathematics Colloquium**Title:**Entropy methods and the SL(2,R) action on Moduli space.**Speaker:**Alex Eskin, Dynamical Systems Speaker, University of Chicago (Host: Boris Kalinin)**Location:**MB114I will outline the first part of my recent proof with Maryam Mirzakhani of the measure classification theorem for this action. This part is an entropy based argument, closely related to that of Einsiedler-Katok-Lindenstrauss and others. (No knowledge of Teichmuller theory is required).

- October 17th, 2014 (03:35pm - 04:35pm)
**Seminar:**Probability and Financial Mathematics Seminar**Title:**TBA**Speaker:**Hongyuan Lu, PSU, Industr. & Manufact. Engineering**Location:**MB106- October 20th, 2014 (03:35pm - 04:35pm)
**Seminar:**Dynamical systems seminar**Title:**TBA**Speaker:**Ke Zhang, University of Toronto**Location:**MB114- October 21st, 2014 (01:00pm - 01:50pm)
**Seminar:**Theoretical Biology Seminar**Title:**Modeling tuberculosis, from cells to populations**Speaker:**Leonid Chindelevitch, MIT

(Host: Tim Reluga)**Location:**MB106Tuberculosis continues to afflict millions of people and causes over a million deaths a year worldwide. Multi-drug resistance is also on the rise, causing concern among public-health experts. This talk will give an overview of my work on modeling tuberculosis at various scales. On the cellular side I will describe models of the metabolism of M. tuberculosis, where insights from duality led to a consistent analysis of existing models, a systematic method for reconciling discrepant models, and the identification of putative drug targets. On the population side I will describe models of strain evolution, where a new metric combined with an optimization-based approach resulted in an accurate classification of complex infections as originating from mutation or mixed infection, as well as the identification of the strains composing these complex infections.

- October 21st, 2014 (02:30pm - 03:45pm)
**Seminar:**Logic Seminar**Title:**To be announced**Speaker:**Jeremy Avigad, Carnegie Mellon University**Location:**MB315- October 21st, 2014 (03:30pm - 06:00pm)
**Seminar:**Working Seminar: Dynamics and its Working Tools**Title:**Invariant distributions for dynamical systems,III (tentative)**Speaker:**Alejandro Kocsard, Fluminense Federal University, Brazil**Location:**MB216- October 22nd, 2014 (03:35pm - 04:25pm)
**Seminar:**Teaching Mathematics Discussion Group Seminar**Title:**Opportunities for Theoretical Thinking**Speaker:**Attendees, Penn State**Location:**MB102The majority of lower-level curriculum provides little in the way of theoretical assignments. Is it, however, possible to incorporate activities that encourage high-level thinking in 100- or 200-level curriculum? This week, we read a paper that explores this issue and we consider if its suggestions could be realistically incorporated into the classroom.

Challita, Dalia, and Nadia Hardy. "Providing calculus students with opportunities to engage in theoretical thinking."*16TH Annual Conference on Research in Undergraduate Mathematics Education*1 (n.d.): 16-30. Web. 20 Aug. 2014.- October 23rd, 2014 (01:25pm - 02:25pm)
**Seminar:**MASS Colloquium**Title:**Evolution of resistance to white pine blister rust in high-elevation pines**Speaker:**Simon Tavener, Colorado State University**Location:**MB114Five-needle white pines play an important role in high-elevation ecosystems but are highly susceptible to white pine blister rust (WPBR) caused by a nonnative fungal pathogen. We construct a nonlinear, stage-structured infection model to investigate the effect of WPBR on the dynamics and stand structure of high-elevation five-needle white pines. Management decisions are by definition short-term perturbations that require analysis of transient behavior and we have developed a general software package to examine both transient and equilibrium sensitivities and elasticities. The presence in a population of a resistant genotype can modify both transient and equilibrium behaviors and suggest potential new control strategies. We extend our model to include a resistant allele at a single genetic locus and provide preliminary results. This work was conducted as part of an NSF sponsored undergraduate research program (FEScUE) at the intersection of mathematics and biology.

- October 23rd, 2014 (03:30pm - 04:20pm)
**Seminar:**Department of Mathematics Colloquium**Title:**A posteriori error analysis for multirate, multiphysics problems**Speaker:**Simon Tavener, Colorado State University (Host: Andrew Belmonte)**Location:**MB114Finite element methods are well-established and popular techniques for solving systems of partial differential equations. A priori analyses of finite element methods seek to establish error bounds in appropriate norms and to determine rates of convergence with mesh refinement. Adjoint-based a posteriori analyses seek to estimate the error in a functional of the solution (a “quantity of interest”) for a given numerical calculation. Computation plays an essential role in many areas of science and technology where we seek to understand complex systems involving multiple physical processes which often evolve on distinctly different time scales. Complicating matters, the model parameters and even computational domains may be uncertain. Further, specific numerical approaches such as finite volume methods or explicit time integration techniques may be entrenched within particular scientific communities. The goal of this work is to use mathematically appealing adjoint-based a posteriori ideas to develop accurate a posteriori error estimates for a range of computational problems encountered in practice and to use the insights gained in to the multiple sources of error to construct adaptive computational strategies.

- October 24th, 2014 (03:35pm - 04:35pm)
**Seminar:**Probability and Financial Mathematics Seminar**Title:**TBA**Speaker:**Jason Morton, PSU**Location:**MB106- October 27th, 2014 (03:35pm - 04:35pm)
**Seminar:**Dynamical systems seminar**Title:**TBA**Speaker:**Rafael de la Llave, Georgia Tech**Location:**MB114- October 28th, 2014 (01:00pm - 01:50pm)
**Seminar:**Theoretical Biology Seminar**Title:**TBA**Speaker:**Georgi Medvedev, Drexel University

(Host: Vladimir Itskov)**Location:**MB106- October 28th, 2014 (02:30pm - 03:30pm)
**Seminar:**Center for Dynamics and Geometry Colloquium**Title:**TBA**Speaker:**Rafael de la Llave, Georgia Tech**Location:**MB114- October 29th, 2014 (03:35pm - 04:25pm)
**Seminar:**Teaching Mathematics Discussion Group Seminar**Title:**Preparing Students for Calculus**Speaker:**Attendees, Penn State**Location:**MB102Last week, we considered ways of preparing calculus students for higher-level classes. This week, we consider what it takes to adequately prepare students for calculus.

Judd, April B., and Terry Crites. "Preparing students for calculus."*16TH Annual Conference on Research in Undergraduate Mathematics Education*1 (n.d.): 96-105. Web. 20 Aug. 2014.- October 30th, 2014 (01:25pm - 02:25pm)
**Seminar:**MASS Colloquium**Title:**TBA**Speaker:**Greg Lawler, University of Chicago**Location:**MB113- October 31st, 2014 (03:30pm - 05:00pm)
**Seminar:**CCMA PDEs and Numerical Methods Seminar Series**Title:**Fractional Sturm-Liouville Eigen-Problems: Theory and Applications to Fractional PDEs in High Dimensions**Speaker:**Mohsen Zayernouri, Brown University**Location:**MB315Fractional Calculus is unifying theory that generalizes the standard (integer-order) calculus to real (fractional-order) differentiation and integration. The corresponding non-local operators of fractional order (in time and/or space) are shown to appear in a wide rang of applications. In continuum-time random walk (CTRW), which allows to incorporate waiting times and/or non-Gaussian jump distributions, the continuous limit leads to the notion of fractional calculus yielding fractional in time and/or space diffusion equation, governing the PDF of the Levy processes. In Bioengineering, there is an extensive amount of experimental evidence that highlights such processes occur in critical applications such as diffusion processes in human brain, cardiac tissue electrode interface, viscoelastic response of human red-blood-cells, wall-arteries, lung tissues, etc. In such power-law attributed phenomena, fractional PDEs naturally appear as the right mathematical framework. extension of existing numrical methods to FPDEs is not trivial because of their non-local and history-dependent nature. To this end, we first present a fractional (regular and singular) Sturm-Liouville eigen-problems, recently developed by Zayernouri & Karniadakis JCP 2013, which serves as a fundamental theory that provides explicit (non-polynomial) eigen-functions, namely as Jacobi Poly-fractonomials. These eigen-functions extend the well-known family of Jacobi polynomials to their fractional counterparts, where we show that they enjoy many attractive properties such as orthogonality, recurrence relations, exact fractional derivatives/integrations, in addition to their spectral properties. Based upon this base fractional theory, we develop a unified Petrov-Galerkin spectral method for solving the whole family of parabolic, elliptic, and hyperbolic (time- and space-) fractional PDEs in any (d+1)-dimensions in a hypercube. While the existing numerical methods can take days to run a One-Dimensional problem, we also formulate a unified fast linear solver for our scheme, which allows one to run a "Ten-Dimensional" FPDE on a laptop within a fractional of an hour!

- October 31st, 2014 (03:35pm - 04:35pm)
**Seminar:**Probability and Financial Mathematics Seminar**Title:**TBA**Speaker:**Alexei Novikov, PSU**Location:**MB106