This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

Conferences and workshops

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  • 23rd Canadian Conference on Computational Geometry.

The conference is dedicated to computational, combinatorial and discrete geometry, as well as work from a wide range of applications, such as graphics, vision, robotics, geographical information systems, protein folding, statistical analysis, graph drawing, visualization, circuit design, etc.

  • Computational topology short course conducted by the American Mathematical Society in New Orleans, January 4 and 5, 2011.
  • Ohio Valley Affiliates for Life Sciences (OVALS) conference, April 15-16, 2010, Louisville, KY
  • Joint AMS-MAA Mathematics Meeting, Washington, DC, January 2009.
  • IMA New Directions Short Course Applied Algebraic Topology at the Institute for Mathematics and Its Applications, University of Minnesota, June 2009.
  • International Conference on Image Processing, Computer Vision, and Pattern Recognition, Las Vegas, Nevada, July 2009.
  • Bio-Image informatics Workshop, Santa Barbara, CA, January 2008.
  • National meeting of the American Society for Cell Biology, Washington, DC, November 2007.
  • Workshop Applications of topology in science and engineering, at Mathematical Sciences Research Institute, Berkeley, CA, September 2006. Talk Homology of color images.

Organized By: G. Carlsson, P. Diaconis, and S. Holmes Parent Programs: Computational Applications of Algebraic Topology. It is becoming increasingly clear that algebraic topology can be applied effectively in to a number of applied problems in science and engineering. Some of these problems are:

  1. Protein docking
  2. Algorithmic and geometric problems in robotics
  3. Exploratory and qualitative analysis of high-dimensional data sets
  4. Coverage and routing problems for networks of sensors
  5. Analysis of chaotic non-linear dynamical systems

The purpose of this workshop is to survey the state of the various applications, to allow the investigators to share ideas about them, and to generate new applications. Both mathematicians as well as practitioners in science and engineering are invited to participate, so that new classes of problems can be proposed as candidates for the use of algebraic topological methods.

  • Computational Topology Workshop, July 14, 2005, Denison University, OH. 2005 Summer Conference on Topology and Its Applications.
  • PREP Geometric Combinatorics Workshop, May 23 – 27, 2004, Mathematical Sciences Research Institute, Berkeley, CA.

The Mathematical Association of America’s PRofessional Enhancement Program (PREP) enables faculty in the mathematical sciences to respond to rapid and significant developments that impact undergraduate mathematics. PREP workshops offer extended professional development experiences with active involvement by all participants, leadership by experts, and a commitment by participants to make use of what they learn. To achieve a sustained impact, PREP workshops extend over time with preparatory, intensive and on-going components. Follow-up components are typically held in conjunction with the Joint Mathematics Meetings each January. The program costs as well as the costs of food and lodging during the workshop are covered by PREP.

Geometric combinatorics refers to a growing body of mathematics concerned with counting properties of geometric objects described by a finite set of building blocks. Polytopes (which are bounded polyhedra) and complexes built up from them are primary examples. Other examples include arrangements of points, lines, planes, convex sets, and their intersection patterns. There are many connections to linear algebra, discrete mathematics, analysis, and topology, and there are exciting applications to game theory, computer science, and biology. The beautiful yet accessible ideas in geometric combinatorics are perfect for enriching courses in these areas. Some of topics we will cover include the geometry and combinatorics of polytopes, triangulations, combinatorial fixed point theorems, set intersection theorems, combinatorial convexity, lattice point counting, and tropical geometry. We will have fun visualizing polytopes and other constructions, and exploring neat applications to other fields such as the social sciences (e.g., fair division problems and voting) and biology (e.g., the space of phylogenetic trees). Many interesting problems in geometric combinatorics are easy to explain, but remain unsolved.

  • IMA New Directions Short Course Computational Topology, July 6-16, 2004 Institute for Mathematics and Applications, Minneapolis, MN. Participation included joint research and a presentation. Participants were selected based on their applications.

2004. Attended the Sectional AMS Meeting in Athens, OH.

  • Knot Theory workshop at Wake Forest University, NC, organizer Colin Adams (Williams College), June 9 – 14, 2003.

Knot theory is a great topic for exciting students about mathematics. It is visual and hands on. Participants can begin working on problems the first day with their shoelaces. Knot theory is also an incredibly active field. There is a tremendous amount of work going on currently, and one can easily state open problems. It also has important applications to chemistry, biochemistry and physics. This workshop is aimed at college and university teachers who are interested in knowing more about knot theory. The goals of the workshop are as follows: 1. Participants will be able to teach an undergraduate course in knot theory. 2. Participants will be able to do research in knot theory. 3. Participants will be able to direct student research in knot theory. Colin Adams is the Francis C. Oakley Third Century Professor of Mathematics at Williams College. He wrote “The Knot Book: an Elementary Introduction to the Mathematical Theory of Knots” and has taught an undergraduate course on knot theory many times. He has published over 30 articles on knot theory and related subjects. He has directed over 40 undergraduate students on research in knot theory and co-authored papers with a total of 33 different undergraduates.

I am aware that this is a very exciting and active area of topology. I would like to expand my horizons to include this area as a potential topic for future teaching and research. The first step in this direction would be this workshop. I think topology should be as prominent in the undergraduate curriculum as algebra or analysis. I would like to develop a topology course accessible to beginning math majors. Such a course should have a very limited set of prerequisites, mostly an appropriate level of "mathematical maturity". I would also like it to be modern and related to current research in topology. A course based on Knot Theory or one with a significant component related to it would definitely serve this purpose. It could become a stepping stone for the development of an undergraduate research program as well as a topic for master theses.

  • Invited talk Lefschetz and Nielsen numbers in Control Theory, at the Joint AMS-MAA Meeting in Phoenix, AZ, January 2004.
  • Talk Higher order Nielsen numbers, at the Conference on Geometric Topology, Xi’an, China, August 2002, as a part of the International Congress of Mathematicians.

It is called the Conference on Geometric Topology, a Satellite Conference of ICM 2002, held at Shaanxi Normal University, Xi'an, China. This conference is organized in conjunction with the International Congress of Mathematicians. These congresses are organized by the International Mathematical Union. They are held every 4 years since1897 and attract thousands of mathematicians from around the world. I was the only person representing Marshall University. The conference was aimed at reflecting the current state of the art in the study of low dimensional topology and related subjects. There were multiple plenary lectures outlining the broad picture of this area of Topology.