USF Home > College of Arts and Sciences > Department of Mathematics & Statistics

Mathematics & Statistics

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On some extremal problems in complex analysis

Alex Stokolos

Georgia Southern University

3:00pm-4:00pm

CMC 130

Dima Khavinson

**Abstract**

Many celebrated results in Complex Analysis state solutions to some extremal problems. For instance, let me mention Koebe one quarter theorem and Bieberbach conjecture (now De Brange Theorem). In the talk I will discuss the polynomial version of these theorems and related questions. The lecture will be accessible to everyone who has taken a standard complex analysis course.

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TBA

Ryan Martin

Iowa State University

3:00pm-4:00pm

CMC 130

Theo Molla

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TBA

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TBA

Driss Bennis

University of Rabat

TBA

TBA

Mohamed Elhamdadi

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TBA

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TBA

Erik Pedersen

Binghamton University

3:00pm-4:00pm

CMC 130

Mohamed Elhamdadi

**Abstract**

TBA

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TBA

Juan Manfredi

University of Pittsburgh

3:00pm-4:00pm

CMC 130

Thomas Bieske

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TBA

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TBA

Jack Lutz

Iowa State University

3:00pm-4:00pm

CMC 130

Nataša Jonoska

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TBA

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TBA

Mizuki Fukuda

Tohoku University

TBA

TBA

Masahico Saito

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TBA

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Ideals Lattices and Applications

Ha Tran

Concordia University of Edmonton

3:00pm-4:00pm

CMC 130

Nataša Jonoska

**Abstract**

Ideal lattices form a powerful tool not only for computational number theory but also for cryptography and coding theory, thanks to their underlying structures that enable a variety of useful constructions. In this talk, we will first discuss ideal lattices and their application in computational number theory such as computing important invariants of a number field (the class number, the class group and the unit group). Then we will discuss an application of ideal lattices in cryptography: constructing cryptosystems that are conjectured to be secure under attacks by quantum computers. An application of ideal lattices in coding theory — minimizing the value of the inverse norm sums — will be presented after that. Finally, we will discuss some open problems relating to this topic.

**References**

- E. Bayer-Fluckiger. Lattices and number fields. In
*Algebraic geometry: Hirzebruch 70 (Warsaw, 1998)*, volume 241 of Contemp. Math., pages 69-84. Amer. Math. Soc., Providence, RI, 1999. - J.-B. Bost. Theta invariants of euclidean lattices and infinite-dimensional hermitian vector bundles over arithmetic curves.
*arXiv preprint arXiv:1512.08946*, 2015. - H. Cohen. A course in computational algebraic number theory, volume 138 of Graduate Texts in Mathematics. Springer-Verlag, Berlin, 1993.
- L. Ducas and A. Durmus. Ring-lwe in polynomial rings. In
*International Workshop on Public Key Cryptography*, pages 34-51. Springer, 2012. - Y. Elias, K. E. Lauter, E. Ozman, and K. E. Stange. Provably weak instances of ring-lwe. In
*Annual Cryptology Conference*, pages 63-92. Springer, 2015. - P. Francini. The size function \(h^0\) for quadratic number fields.
*J. Théor. Nombres Bordeaux*, 13(1):125-135, 2001. 21st Journées Arithmétiques (Rome, 2001). - C. Gentry. Fully homomorphic encryption using ideal lattices. Proceedings of the 41st Annual ACM Symposium on Theory of Computing—STOC'09. vol. 9. 2009.
- O. W. Gnilke, A. Barreal, A. Karrila, H. T. N. Tran, D. A. Karpuk, and C. Hollanti. Well-rounded lattices for coset coding in mimo wiretap channels. In Telecommunication Networks and Applications Conference (ITNAC), 2016 26th International, pages 289-294. IEEE, 2016.
- H. W. Lenstra, Jr. Algorithms in algebraic number theory. Bull. Amer. Math. Soc. (N.S.), 26(2):211-244, 1992.
- H. W. Lenstra, Jr. Lattices. In Algorithmic number theory: lattices, number fields, curves and cryptography, volume 44 of Math. Sci. Res. Inst. Publ., pages 127-181. Cambridge Univ. Press, Cambridge, 2008.
- V. Lyubashevsky, C. Peikert, and O. Regev. On ideal lattices and learning with errors over rings. In Annual International Conference on the Theory and Applications of Cryptographic Techniques, pages 1-23. Springer, 2010.
- V. Lyubashevsky, C. Peikert, and O. Regev. A toolkit for ring-lwe cryptography. In T. Johansson and P. Q. Nguyen, editors, Advances in Cryptology — EUROCRYPT 2013, pages 35-54, Berlin, Heidelberg, 2013. Springer Berlin Heidelberg.

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Means of positive matrices

Raluca Dumitru

University of North Florida

TBA

TBA

Boris Shekhtman

**Abstract**

Matrix means have received a lot of attention in the past years. A notion easy to understand for numbers, it created a lot of interesting problems when extended to positive matrices, due in part to matrix multiplication not being commutative, and secondly because the order relation on positive matrices presents some challenges. In this talk, we will give an introduction to the theory of matrix means and present some of our results related to their geometry, inequalities between matrix means, and characterizations of matrix monotone functions.

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Viji Thomas

Indian Institute of Science Education and Research Thiruvananthapuram

2:00pm-3:00pm

CMC 108

Xiang-dong Hou

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TBA

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Similarity of matrices from an arithmetic point-of-view

Tommy Hofmann

Technische Universität Kaiserslautern

2:00pm-3:00pm

CMC 108

Dima Savchuk

**Abstract**

Similarity of matrices is a fundamental notion in linear algebra and an indispensable tool when investigating linear operators. In this talk we will consider similarity of matrices in connection with arithmetic questions, like the integrality of the matrix entries. By employing tools from number theory and representation theory, we will explain how these problems can be solved both in theory and practice.

This talk will be held in conjunction with the Discrete Mathematics seminar.

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Computational approaches to nonlinear inverse scattering problems

Howard Levinson

University of Michigan

3:00pm-4:00pm

CMC 130

Catherine Bénéteau

**Abstract**

Data obtained from scattering experiments contains valuable information regarding the internal structure of opaque objects. Reconstructing the structure from these potentially large data sets is a difficult computational task. In this talk, I describe two new algorithms for solving this nonlinear inverse scattering problem. The first algorithm directly addresses the issue and is well-suited for large data sets, which are increasingly common with modern experimental techniques. The second algorithm concerns the compressed sensing problem—where sparsity of the target can be used to reduce the necessary number of measurements. In the final part of the talk, I introduce an experimental approach in fluorescence microscopy that can achieve subwavelength resolution from limited data measurements.

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Particle models for boundary coarsening in networks

Joseph Klobusicky

Rensselaer Polytechnic Institute

2:00pm-3:00pm

CMC 109

Sponsor Name

**Abstract**

We construct a family of stochastic particle systems which models the coarsening of two-dimensional networks through mean curvature. The limiting kinetic equations of these models, describing distributions of grain areas and topologies, are shown to be well-posed. Evidence for the exponential convergence of the empirical densities of the particle system to solutions of the kinetic equations is provided through several minimal models. The framework for the particle system is general enough to allow for various assumptions proposed in the 1980’s and 1990’s concerning facet exchange and first order neighbor correlations. Particle system models for several different assumptions are compared against direct simulations.

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Optimal Transport and Topology in Data Science

Thomas Needham

Ohio State University

11:00am-12:00pm

CMC 109

K. Ramachandran

**Abstract**

The optimal transport problem seeks the cost-minimizing plan for moving materials to building sites. It was first formulated precisely by Monge in the 1700s and has since developed into its own sophisticated subfield of pure mathematics. Recent advances in theory and algorithm design have transformed optimal transport into a viable tool for analyzing large datasets. In this talk, I will describe a way to compare general abstract metric spaces using ideas from optimal transport and demonstrate an application to feature matching of anatomical surfaces. Along the way, I will formulate several natural inverse problems in geometry and graph theory whose solutions are obtained via tools from the rapidly-developing field of topological data analysis.

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Interfaces between Reproducing Kernel Herbert Spaces, Systems Theory, and Optimal Control

Joel Rosenfeld

Vanderbilt University

2:00pm-3:00pm

CMC 109

Razvan Teodorescu

**Abstract**

In this talk we will examine connections between data science, systems theory and optimal control. The talk will discuss various aspects of reproducing kernel Hilbert spaces, including densely defined multiplication operators and an approximation framework for the online estimate of an approximate optimal controller. Finally, the talk will conclude by demonstrating a connection between densely defined operators over reproducing kernel Hilbert spaces and optimal control theory through a new kernel function inspired by occupation measures.

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Using functional data analysis to exploit high-resolution “Omics” data

Marzia Cremona

Pennsylvania State University

3:30pm-4:30pm

CMC 120

Catherine Bénéteau

**Abstract**

Recent progress in sequencing technology has revolutionized the study of genomic and epigenomic processes, by allowing fast, accurate and cheap whole-genome DNA sequencing, as well as other high-throughput measurements. Functional data analysis (FDA) can be broadly and effectively employed to exploit the massive, high-dimensional and complex “Omics” data generated by these technologies. This approach involves considering “Omics” data at high resolution, representing them as “curves” of measurements over the DNA sequence.

I will demonstrate the effectiveness of FDA in this setting with two applications.

In the first one, I will present a novel method, called probabilistic K-mean with local alignment, to locally cluster misaligned curves and to address the problem of discovering functional motifs, i.e., typical &ldquol;shapes” that may recur several times along and across a set of curves, capturing important local characteristics of these curves. I will demonstrate the performance of the method on simulated data, and I will apply it to discover functional motifs in “Omics” signals related to mutagenesis and genome dynamics.

In the second one, I will show how a recently developed functional hypothesis test, IWTomics, and multiple functional logistic regression can be employed to characterize the genomic landscape surrounding transposable elements, and to detect local changes in the speed of DNA polymerization due to the presence of non-canonical 3D structures.