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Convex Algebraic Geometry
Applied and Computational Topology
Discrete Probability on Surfaces
Combinatorics and Matrices
Mathematics and Systems Biology
Walk the Walk, Talk the Talk
Thursday afternoon, Ballroom C
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Convex algebraic geometry centers around the interplay between algebraic geometry, classical convexity, and optimization. Algebraic geometry provides necessary tools to analyze and develop solutions to optimization problems, and solvers for convex optimization have led to new fast algorithms in real algebraic geometry.
Saturday afternoon, Ballroom D
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One of the exciting recent developments in applied mathematics has been the explosion of insights, techniques, and tools from algebraic topology that have been used to great advantage in examining computation problems in data analysis, distributed networks, and dynamical systems. This special session will feature eight presentations on various aspects of a subject that encourages collaborations and synergies between mathematicians, statisticians, biologists, chemists, physicists, materials scientists, and computer scientists. In total, the session should provide a broad introduction to the area with a balance between the theory and applications.
Saturday afternoon, Ballroom C
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Thursday afternoon, Ballroom C
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This session will focus on the substantial interaction between combinatorics, graph theory, and matrix theory.
Saturday afternoon, Ballroom B
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Systems biology is the study of the systems-level understanding and analysis of the biology, behavior and interactions between the biology and behavior at all levels of biological organization from the small scales of molecules and cells up to the large scales of populations and communities. Systems biology is interdisciplinary by nature, and employs significant mathematical and computational techniques to model and analyze complex biological systems. The mathematics involved in modeling complex systems is wide and varied and includes not only differential equations but also Boolean dynamics, contact networks, individual based modeling, and algebraic techniques. Examples of areas of study of gene system analysis and epidemic modeling. This session will focus on the applications of mathematics to research in areas of systems biology.
Friday afternoon, Ballroom C
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This session will feature talks on walks on lattices and graphs and some of their many applications in enumerating tableaux, pattern-avoiding permutations, random walks, Markov chains, and many other constructs.