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Lorinda Leshock | Lorinda Leshock | Ewing 336 | Title: Configurations in Finite Planes: Combinatorics and Analytic Geometry <br><br> Abstract: Finite planes are combinatorial objects that may be studied from a geometric viewpoint with implications for algebraic systems. In this talk, we define finite affine and projective planes and present examples of coordinatized affine planes. We discuss the implications of the existence of Desargues’ and Pappus’ configurations in these planes and provide a short combinatorial proof (due to Ostrom) that Desargues’ configuration exists in all finite projective planes of order greater than 3. We conclude by stating a strong result for the existence of Pappus’ configurations in Hall projective planes. (This is joint work with Felix Lazebnik.) | 10/10/2018 4:00:00 PM | 10/10/2018 5:00:00 PM | False | |

Emily Bergman | Emily Bergman | EWG 336 | Title: Secondary Constructions of PN and APN Functions Abstract: Highly non-linear functions are important in cryptology as they provide security against differential cryptanalysis. Differential uniformity is a measure of a function's linearity, with highly non-linear functions having low differential uniformity. There is a natural lower bound for the differential uniformity of any function, and functions over finite fields that are optimal with respect to this bound are known as perfect nonlinear (PN) for odd characteristic, and almost perfect nonlinear (APN) for even characteristic. We shall discuss the concept of differential uniformity, and PN and APN functions. In particular, our goal is to develop secondary constructions for functions with low differential uniformity; in other words we want to develop methods by which a given PN or APN function can be altered to obtain a new function with low differential uniformity, preferably optimal. We will discuss previous research, including connections with mutually orthogonal systems, along with our initial attempts to develop a secondary construction. | 10/3/2018 4:00:00 PM | 10/3/2018 5:00:00 PM | False | |

Multiple Speakers | Multiple Speakers | EWG 336 | Title: "What I Did At Summer School"<br> Abstract: This is a presentation of multiple things that students did in the summer. Students will discuss different opportunities and have question and answer about each. | 9/26/2018 3:00:00 PM | 9/26/2018 4:00:00 PM | False | |

Bradley Fain | Bradley Fain | EWG 336 | Title: Some Power Mappings With Low Differential Uniformity Abstract: In this talk we will look at differentially uniform power mappings over Fpn of the form f(x) = x d . A mapping f(x) is called differentially k-uniform if the number of solutions, x, to the equation f(x + a) − f(x) = b is bounded above by k for all a, b ∈ Fpn with a 6= 0. When p = 2, a construction for an infinite family of 2-uniform mappings is given. For p 6= 2, two large families of k-uniform mappings are constructed with low values of k. We will also see a way to construct families of sequences with good correlations from differentially 1-uniform mappings. | 9/19/2018 4:00:00 PM | 9/19/2018 5:00:00 PM | False |

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