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Seminars will usually take place on Wednesdays, 9am - 10am in Ewing 336. Consult the schedule for more details. For more information, contact our seminar coordinator Sebastian Cioaba.
| Evan DeCorte, McGill University | Evan DeCorte, McGill University | EWG 336 | Title: The hyperbolic Hadwiger-Nelson problem<br> <br>
Abstract: Consider the graph H(d) whose vertex set is the hyperbolic plane, where we join two points with an edge when their distance is equal to d. Asking for the chromatic number of this graph is the hyperbolic analogue to the famous Hadwiger-Nelson problem about colouring the Euclidean plane. As in the Euclidean case, one can lower bound the chromatic number of H(d) by 4 for all d. Using spectral methods, we prove that if the colour classes are measurable, then at least 6 colours are needed to properly colour H(d) when d is sufficiently large. This can be regarded as the hyperbolic analogue of Falconers lower bound for the measurable chromatic number of the plane. Joint work with Konstantin Golubev. In addition to discussing the result, an aim of this talk will be to survey the spectral method for infinite graphs. | 9/20/2017 1:00:00 PM | 9/20/2017 2:00:00 PM | False | |
| Glenn Hurlbert, Virginia Commonwealth University | Glenn Hurlbert, Virginia Commonwealth University | Ewing 336 |
"Injective Proofs of the Erdos-Ko-Rado and Hilton-Milnor Theorems" <br><br>
Let F be a family of r-subsets of {1,2,...,n}. We say that F is intersecting if every pair of its sets intersect. The special case when some element (its center) is in each of its sets is called a star. The Erdos-Ko-Rado Theorem (1961 [really 1938]) states that, when n>2r, the largest intersecting family is a star. The Hilton-Milnor Theorem (1967) states that, when n>2r, the largest non-star intersecting family is a near-star: a star with an extra set not containing its center. Vikram Kamat and I recently devised the first injective proofs of these classical results. I will share them with you in this talk. | 9/27/2017 1:00:00 PM | 9/27/2017 2:00:00 PM | False | |
| Eric Moorhouse, University of Wyoming | Eric Moorhouse, University of Wyoming | Ewing 336 | TBA | 10/25/2017 1:00:00 PM | 10/25/2017 2:00:00 PM | False | |
| Huda Chuangpishit, Carleton University, Canada | Huda Chuangpishit, Carleton University, Canada | EWG 336 | TBA | 11/8/2017 2:00:00 PM | 11/8/2017 3:00:00 PM | False | |
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