Val Soltan Professor Office: Science & Technology Building I, Room 241 Phone: (703) 993-1474 Fax: (703) 993-1491 E-mail: vsoltan@gmu.edu

Degree

• Dr., 1985, Academy of Sciences of Moldova, Generalized Convexity.

Research

Convex and Discrete Geometry:

• convex sets in n dimensions
• special classes of convex sets
• various problems of discrete geometry

Teaching

• This semester courses

Some Recent Papers

• Convex sets with homothetic projections, Beiträge Algebra Geom. 51 (2010) and arXiv:0903.2836v1, 2009. [pdf]

• Convex solids with planar homothetic sections through given points, J. Convex Anal. 16 (2009), 473-486. [pdf]

• The intersection of convex transversals is a convex polytope, Beiträge Algebra Geom. 50 (2009), 283-294 (with J. Lawrence). [pdf]

• Convex solids with planar midsurfaces, Proc. Amer. Math. Soc. 136 (2008), 1071-1081. [pdf]

• Line-free convex bodies with centrally symmetric intersections of translates, Rev. Roumaine Math. Pures Appl. 51 (2006), 111--123. [pdf]

• Isothetic parallelotopes and the binary intersection property, Acta Sci. Math. (Szeged) 72 (2006), 373--385. [pdf]

Books and Selected Surveys

• The Erdös-Szekeres problem on points in convex position--a survey, Bull. Amer. Math. Soc. 37 (2000), 437-458 (with W. Morris). [pdf]

• Combiatorial problems on the illumination of convex bodies, Aequationes Math. 57 (1999), 121-152 (with H. Martini). [pdf]

• Geometric methods and optimization problems, Kluwer Academic Publishers, Combinatorial Optimization Series, 1998, 429 pp. (with V. Boltyanski and H. Martini).

• Introduction to the axiomatic theory of convexity, Stiinta, Chisinau, 1984, 224 pp.

Presentations

• Invited talks at Courant and Polytechnic Institutes of New York University (2009).

• Invited talks at University College London, Rényi Institute of Mathematics, Universities of Technology in Dresden, Chemnitz, and Munich (all in the fall of 2007).

• AMS Meetings: Middletown, CT (2008), Vancouver, BC (2008), Hoboken, NJ (2007), Durham, NH (2006), Pittsburgh, PA (2004), Lawrenceville, NJ (2004), San Francisco, CA (2003), Baltimore, MD (2003), Boston, MA (2002).

• Banff workshops: Transversal and Helly-type theorems (2009), Intuitive geometry (2007), Convex sets and their applications (2006), Convex and abstract polytopes (2005).

Awards

• Various research grants from DAAD, DFG, HHS (all German science foundations), Royal Society of Sweden, Hungarian and Romanian Academies.

• First prize laureate of the Academy of Sciences of Moldova (1980).

Activities

• Member of the editorial board of Beiträge zur Algebra und Geometrie (Contributions to Algebra and Geometry).
• Coorganizer of AMS special sessions: Convex and discrete geometry (Washington, D.C., 2009), Convex sets (Hoboken, NJ, 2007), Recent trends in convex and discrete geometry (San Antonio, TX, 2006), Convexity and combinatorics (Pittsburgh, PA, 2004).

Ph.D. Students

• Sorin Revenko, Helly-type theorems on the existence of support lines for families of convex bodies in the plane, 2002.
• Iacob Ceban, Combinatorial extremal problems in graphs and their applications, 1995.
• Anatolie Sochirca, d-convex analysis in triangulated graphs, 1995.
• Anatolie Prisacaru, Special decompositions of geometric objects into minimum number of convex sets, 1994.
• Alexei Gorpinevich, Partitions of polygonal regions into convex pieces, 1993.
• Manh Hung Nguyen, Affine diameters of convex bodies, 1990.