| Po-Shen Loh, Carnegie Mellon University | Po-Shen Loh, Carnegie Mellon University | Gore 116 | Title: Setting Personalized Learning Free
<br>
Abstract: Improving math and science education is a national priority. Personalized
education is within reach and has the potential to transform current
practices through the usage of data and algorithms. Po-Shen Loh will speak
about the social enterprise he founded (expii.com) that will turn every
smartphone into a free personalized learning system by combining
crowdsourcing and mathematical algorithms. In a modern world where content
is everywhere (but of varying quality, and disorganized), the central
problem is to identify exactly which piece of content a particular learner
should interact with at any given moment based upon the learner’s current
knowledge base and long-term goals. Leveraging the Elo rating system from
competitive chess, Expii introduces a new mathematical framework for
answering this question, which casts the central problem into a graph
algorithm problem.
In this talk, Po-Shen Loh will speak about his experience translating the
mathematics and algorithms from the research world to the practical world,
through mission-driven entrepreneurship. | 4/20/2018 7:30:00 PM | 4/20/2018 9:00:00 PM | False | |
| Po-Shen Loh, Carnegie Mellon University | Po-Shen Loh, Carnegie Mellon University | Memorial Hall 123 | Title: Ramsey Theory and Paths
<br>
Abrstract: Starting from an innocent Ramsey-theoretic question regarding directed
paths in graphs, we discover a series of rich and surprising connections
that lead into the theory around a fundamental result in Combinatorics:
Szemeredi's Regularity Lemma, which roughly states that every graph (no
matter how large) can be well-approximated by a bounded-complexity
pseudorandom object. Using these relationships, we prove that every
coloring of the edges of the transitive N-vertex tournament using three
colors contains a directed path of length at least sqrt(N) e^{log^* N}
which entirely avoids some color. The unusual function log^* is the
inverse function of the tower function (iterated exponentiation). | 4/20/2018 2:30:00 PM | 4/20/2018 3:30:00 PM | False | |
| Ariel Keller, Emory University | Ariel Keller, Emory University | Ewing 336 | Title; "On Cycles, Chorded Cycles, and Degree Conditions,"
<br></br>
Abstract: Sufficient conditions to imply the existence of different substructures in a graph have long
been of interest in graph theory, and conditions that guarantee a large set of cycles or
chorded cycles are a recurring theme. This talk explores different degree sum conditions
that are sufficient for finding a large set of vertex-disjoint cycles or a large set of vertexdisjoint
chorded cycles in a graph.
For an integer t ≥ 1, let σt(G) be the smallest sum of degrees of t independent vertices
of G. We prove that if a graph G has sufficiently large order and degree sum condition
σ4(G) ≥ 8k−3, with k ≥ 2, then the graph contains k vertex-disjoint cycles. We consider an
equivalent condition for chorded cycles, and we prove that the degree sum condition in each
result is sharp. Finally, we conjecture generalized degree sum conditions on σt(G) for t ≥ 2
sufficient to imply that G contains k vertex-disjoint cycles for k ≥ 2 and k vertex-disjoint
chorded cycles for k ≥ 2. This is joint work with Ronald J. Gould and Kazuhide Hirohata. | 4/17/2018 7:30:00 PM | 4/17/2018 8:30:00 PM | False | |
| Novi Bong, University of Delaware | Novi Bong, University of Delaware | Ewing 336 | Title: Degree/Diameter Problem
<br></br>
Abstract: The degree/diameter problem is a problem to determine the largest graphs or
digraphs of given maximum degree and given diameter. The general upper bounds
for this problem are called the Moore bounds and the graphs that attain the bounds
are called Moore graphs. However, there are not many of them.
The research in this area focuses on two approaches, which are finding a tighter
upper bounds for the maximum possible number of vertices or constructing large
graphs of given degree and diameter to improve the lower bounds.
In this talk, I will give an overview about the degree/diameter problem.
| 4/10/2018 7:30:00 AM | 4/10/2018 8:30:00 AM | False | |
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