Math Department
https://wp0.vanderbilt.edu/math
College of Arts and Science | Vanderbilt UniversityTue, 22 Jan 2019 19:10:38 +0000en-UShourly1https://wordpress.org/?v=4.9.8146940276Packing and Covering Directed Triangles
https://wp0.vanderbilt.edu/math/2019/01/packing-and-covering-directed-triangles/
Tue, 22 Jan 2019 19:10:38 +0000https://wp0.vanderbilt.edu/math/?p=8720We prove that if a directed multigraph D has at most t pairwise arc-disjoint directed triangles, then there exists a set of less than 2t arcs in D which meets all directed triangles in D, except in the trivial case t=0. This answers affirmatively a question of Tuza from 1990. This is joint work with Jessica McDonald and Craig Tennenhouse.
]]>8720Special Colloquium
https://wp0.vanderbilt.edu/math/2019/01/special-colloquium-12/
Mon, 21 Jan 2019 21:10:29 +0000https://wp0.vanderbilt.edu/math/?p=8722Tea at 2:30 pm in Stevenson 1425.
]]>8722Directly representable varieties, decidable varieties, varieties with few models; characterizations
https://wp0.vanderbilt.edu/math/2019/01/directly-representable-varieties-decidable-varieties-varieties-with-few-models-characterizations/
Mon, 14 Jan 2019 22:10:44 +0000https://wp0.vanderbilt.edu/math/?p=8689I will present the characterization of locally finite varieties with only a finite number of directly indecomposable members, and take a walk around the other topics.
]]>8689Equivalent Definitions of Property (T)
https://wp0.vanderbilt.edu/math/2019/01/equivalent-definitions-of-property-t/
Mon, 14 Jan 2019 22:10:29 +0000https://wp0.vanderbilt.edu/math/?p=8700We will give some definitions of Property (T) and show that they are equivalent. (This is the first talk in a semester-long series on SL(3,Z) and Property (T).)
]]>8700The even-faced genus of complete graphs and the Even Map Color Theorem
https://wp0.vanderbilt.edu/math/2019/01/the-even-faced-genus-of-complete-graphs-and-the-even-map-color-theorem/
Mon, 14 Jan 2019 21:10:51 +0000https://wp0.vanderbilt.edu/math/?p=8697The well-known Map Color Theorem extends the Four Color Theorem by providing a sharp bound for the chromatic number of a graph embeddable in a given surface. The bound was found by Heawood in 1890, but it took another 78 years to find all of the sharpness examples, using minimum genus embeddings of complete graphs. In 1975 Joan Hutchinson showed that a graph with an embedding in a given surface with all faces of even degree satisfies a stronger bound on its chromatic number. We have recently determined the minimum genus, both orientable and nonorientable, of embeddings of complete graphs in which all faces have even degree. These embeddings, and embeddings derived from them, provide sharpness examples for Hutchinson’s bound except for a couple of surfaces of small genus. Thus, we now have a sharp Even Map Color Theorem. This is joint work with Beifang Chen, Nora Hartsfield, Serge Lawrencenko, Wenzhong Liu, Hui Yang, Dong Ye and Xiaoya Zha.
]]>8697Talk Title TBA
https://wp0.vanderbilt.edu/math/2019/01/talk-title-tba-265/
Fri, 11 Jan 2019 22:10:04 +0000https://wp0.vanderbilt.edu/math/?p=86078607Hyperbolic Structures on Wreath Products
https://wp0.vanderbilt.edu/math/2019/01/hyperbolic-structures-on-wreath-products/
Wed, 09 Jan 2019 22:10:41 +0000https://wp0.vanderbilt.edu/math/?p=8617The poset of hyperbolic structures on a group G is still very far from being understood and several questions remain unanswered. In this talk, I will speak about some new results that describe hyperbolic structures on the wreath product Gwr Z, for any group G. As a consequence, I answer two open questions regarding quasi-parabolic structures: I will give an example of a group G with an uncountable chain of quasi-parabolic structures and give examples of groups that have finitely many quasi-parabolic structures.
]]>8617Professor Emeritus Horace Williams Dies
https://news.vanderbilt.edu/2019/01/07/horace-williams-emeritus-professor-of-mathematics-dies/?utm_source=myvupreview&utm_medium=myvu_email&utm_campaign=myvupreview-2019-01-07
Mon, 07 Jan 2019 22:10:48 +0000https://wp0.vanderbilt.edu/math/?p=86468646Organizational meeting: Semester on SL(3,Z) and Property (T)
https://wp0.vanderbilt.edu/math/2019/01/organizational-meeting-semester-on-sl3z-and-property-t/
Mon, 07 Jan 2019 22:10:21 +0000https://wp0.vanderbilt.edu/math/?p=8623This semester, we will be running a special series featuring different proofs that SL(3,Z) has Property (T). At this organizational meeting, we will list the known proofs and provide references, and participants can choose which proofs they would like to present.
]]>8623Winter Break: December 24, 2018 – January 2, 2019
https://wp0.vanderbilt.edu/math/2019/01/8597/
Thu, 03 Jan 2019 05:59:57 +0000https://wp0.vanderbilt.edu/math/?p=8597The math administrative office will be observing Winter Break December 24, 2018 – January 1, 2019. Normal office hours will resume on Wednesday, January 2, 2019
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