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seminars:alge [2019/03/26 00:11]
seminars:alge [2019/09/09 07:43] (current)
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-~~META:​title=Algebra Seminar~~+~~META:​title=Fall 2019~~
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-=====Spring ​2019=====+=====Fall 2019=====
 +   * **August 27**\\ Organizational meeting
 +   * **September 3**\\ <​html>​ <span style="​color:​blue;​font-size:​120%">​Casey Donoven </​span></​html>​(Binghamton University) \\ **//​Automata acting on Fractal Spaces//** \\    \\  <WRAP center box 90%> **//​Abstract//​**:​ A self-similar set is a set that is a union of scaled copies of itself. ​ Through iterated labeling of the $n$ copies, $n^2$ subcopies, and so on, we create a correspondence between infinite sequences over an n letter alphabet and points in the self-similar set.  Automata act naturally on infinite sequence, and I will explore groups of homeomorphisms of semi-similar sets induced by automata. ​ I will focus on two examples, the unit interval and Julia set associated to the map $z^2+i$. ​ An important tool in the construction of the automata is the approximation of these self-similar sets as finite graphs. ​
-   * **January 22**\\ ​ <​html>​ <span style="​color:​blue;​font-size:​120%">​Organizational Meeting</​span></​html>​ \\      **//Title of Talk//** \\    \\  <WRAP center box 90%> **//​Abstract//​**:​ Please come or contact the organizers if you are interested in giving a talk this semester or want to invite someone. 
 </​WRAP>​ </​WRAP>​
 +   * **September 10**\\ <​html>​ <span style="​color:​blue;​font-size:​120%">​Matt Evans </​span></​html>​(Binghamton University) \\ **//​BCK-algebras and generalized spectral spaces
 +//** \\    \\  <WRAP center box 90%> **//​Abstract//​**:​ Commutative BCK-algebras are the algebraic semantics of a non-classical logic. Mimicing the
 +construction of the spectrum of a commutative ring (or Boolean algebra or distributive lattice),
 +we can construct the spectrum of a commutative BCK-algebra.
 +A topological space is called *spectral* if it is homeomorphic to the spectrum of some commutative
 +ring, and *generalized spectral* if it is homeomorphic to the spectrum of a distributive lattice
 +with 0.
-   * **January 29**\\ ​ <​html>​ <span style="​color:​blue;​font-size:​120%">​Ben Brewster (Binghamton University) </​span></​html>​ \\      **//The values ​of the Chermak-Delgado measure//** \\    \\  <WRAP center box 90%> **//​Abstract//​**:​ Let $G$ be a finite group. For $H\leq G$$m_G(H) = |H|\ |C_G(H)|$. Let $m^*(G) = max\{m_G(H)\mid H\leq G\}$ and $CD(G) = \{H\leq G\mid m_G(H)=m^*(G)\}$. Then $CD(G)$ is a self-dual modular sublattice of the subgroup lattice of $G$. +In this talk I will briefly discuss Hochster'​s characterization ​of spectral spaces, and then show 
- +that the spectrum ​of a commutative BCK-algebra ​is generalized spectral.
-It is known that if $|G| > 1$, then not every subgroup ​of $G$ is member of $CD(G)$, that is, $|\{m_G(H)\mid H\leq G\}| > 1$. Following some ideas of M. Tarnauceanu,​ we examine possibilities for $|\{m_G(H)\mid H\leq G\}|$, its form and the distribution of subgroups of same measure.+
 </​WRAP>​ </​WRAP>​
- +   * **September 17**\\ <​html>​ <span style="​color:​blue;​font-size:​120%">​Jonathan Doane </​span></​html>​(Binghamton University) ​\\ **// Dualizing Kleene Algebras//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​It is well-known that the class of Boolean algebras is "​generated"​ by 
-   * **February 5**\\  <​html>​ <span style="​color:​blue;​font-size:​120%">​Alex Feingold (Binghamton University)</​span></​html>​ \\      **//An introduction to Lie algebras//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​A Lie algebra ​is a vector space equipped with a bilinear product, denoted by $[\cdot,\cdot]$, such that $[x,x]=0and $[x,[y,z]] + [y,[z,x]] + [z,[x,y]] = 0$ (Jacobi Identity)will give an introduction ​to the basic ideas and examples.+the two element chain $F<​T$ ​equipped with negation ​$\neg F:= T$$\neg 
 +When we include an uncertainty element $F<​U<​T$, along with negation $\neg 
 +U: =U$, we generate the class of Kleene algebras. 
 +Of coursethere is a famous correspondence between Boolean algebras and 
 +Boolean topological spacesnamed Stone duality; 
 +this leads us to wonder if we can somehow represent Kleene algebras by 
 +topological spaces as well. 
 +In factStone duality is but an application of a more general theory of 
 +dual equivalences between categories. 
 +In this talk, we will utilize this theory ​to construct a dual equivalence 
 +between ​the categories of Kleene algebras 
 +and certain topological spaces.
 </​WRAP>​ </​WRAP>​
-   * **February 12**\\  <​html>​ <span style="​color:​blue;​font-size:​120%">​Canceled due to inclement weather ​</​span></​html> ​\\    +   * **September 24**\\ <​html>​ <span style="​color:​blue;​font-size:​120%">​David Biddle ​</​span></​html>​(Binghamton University) \\ **//Title//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​Abstract
- +
- +
-   * **February 19**\\ ​ <​html>​ <span style="​color:​blue;​font-size:​120%">​Daniel Rossi (Binghamton University)</​span></​html> ​\\      **//The structure of finite groups with exactly three rational-valued +
-irreducible characters//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​Many results in the character theory of finite groups are motivated from the question: to what extent do the irreducible characters +
-of a group $G$ control the structure of $G$ itself? Recently, it has been observed that certain results along these lines can be obtained when one looks not at the set of all irreducible characters of $G$, but only the subset of those characters taking values in some appropriate field. In this talk, I'll characterize the structure of finite groups which have exactly three rational-valued irreducible characters (for solvable groups, this characterization is due to J. Tent). I will attempt to give some of the flavor of the proof -- which at one point includes a surprise cameo by the complex Lie algebra $sl(n)$.+
 </​WRAP>​ </​WRAP>​
- +   * **October 1**\\ <​html>​ <span style="​color:​blue;​font-size:​120%">​No Classes ​</​span></​html>​(University) ​\\ **//Title//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​Abstract
-   * **February 26**\\  <​html>​ <span style="​color:​blue;​font-size:​120%">​Casey Donoven (Binghamton University)</​span></​html>​ \\      **//Thompson'​s Group $V$ and Finite Permutation Groups//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​Thompson'​s group $V$ is group of homeomorphisms of Cantor space. ​ It acts by exchanging finite prefixes in infinite strings over a two-letter alphabet. Generalizations of $V$ called $V_n$ act on n-letter alphabets. I will present more generalizations that add the action of finite permutation groups to the finite prefix exchanges. For a finite permutation group $G$ on $n$ points, the group $V_n(G)$ marries the finite prefix exchanges with iterated permutations from $G$. The primary theorem I will present states that $V_n$ is isomorphic to $V_n(G)$ if and only if $G$ is semiregular (i.e. $G$ acts freely). ​ The proof involves the use of automata and orbit dynamics.+
 </​WRAP>​ </​WRAP>​
- +   * **October 8**\\ <​html>​ <span style="​color:​blue;​font-size:​120%">​Ben Brewster ​</​span></​html>​(Binghamton University) ​\\ **//Title//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​Abstract
-   * **March 5**\\  <​html>​ <span style="​color:​blue;​font-size:​120%">​Matt Evans (Binghamton University)</​span></​html>​ \\      **//Spectra of cBCK-algebras//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​BCK-algebras are algebraic structures that come from a non-classical logic. Mimicking a well-known construction for commutative rings, we can put a topology on the set of prime ideals of a commutative BCK-algebra;​ the resulting space is called the spectrum. I will discuss some results/​properties of the spectrum of such algebras. A particularly interesting spectrum occurs when the underlying algebra is a so-called BCK-union of a specific algebra. In this case, the spectrum is a spectral space, meaning it is homeomorphic to the spectrum of a commutative ring.+
 </​WRAP>​ </​WRAP>​
- +   * **October 15**\\ <​html>​ <span style="​color:​blue;​font-size:​120%">​Fikreab Admasu ​</​span></​html>​(Binghamton University) ​\\ **//Title//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​Abstract
-   * **March 12**\\  <​html>​ <span style="​color:​blue;​font-size:​120%">​Hung Tong-Viet (Binghamton University)</​span></​html>​ \\      **//Real conjugacy class sizes and orders of real elements//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​In this talk, I will present some recent results concerning the structure of finite groups with restriction on the real conjugacy classes or on the orders of real elements.  +
 </​WRAP>​ </​WRAP>​
-   * **March 19**\\  <​html>​ <span style="​color:​blue;​font-size:​120%">​Spring Break</​span></​html>​ \\      **//No  Talk//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​Text of Abstract+   * **October 22**\\ <​html>​ <span style="​color:​blue;​font-size:​120%">​Eran Crockett ​</​span></​html>​(Binghamton University) ​\\ **//Title//** \\    \\  <WRAP center box 90%> **//​Abstract//​**:​ Abstract
 </​WRAP>​ </​WRAP>​
-   * **March 26**\\  <​html>​ <span style="​color:​blue;​font-size:​120%">​No Talk</​span></​html>​ \\      **//​Title ​of Talk//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​Text of Abstract+   * **October 29**\\ <​html>​ <span style="​color:​blue;​font-size:​120%">​Speaker ​</​span></​html>​(University) ​\\ **//​Title//​** \\    \\  <WRAP center box 90%> **//​Abstract//​**:​ Abstract
 </​WRAP>​ </​WRAP>​
- +   * **November 5**\\ <​html>​ <span style="​color:​blue;​font-size:​120%">​Luise Kappe </​span></​html>​(Binghamton University) ​\\ **//​Title//​** \\    \\  <WRAP center box 90%> **//​Abstract//​**:​ Abstract
-   * **April 2**\\  <​html>​ <span style="​color:​blue;​font-size:​120%">​John Brown (Binghamton University)</​span></​html>​ \\      **//​Title ​of Talk//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​Text of Abstract+
 </​WRAP>​ </​WRAP>​
-   * **April 9**\\  <​html>​ <span style="​color:​blue;​font-size:​120%">​Jonathan Doane (Binghamton University)</​span></​html>​ \\      **//Restriction of Stone Duality to Generalized Cantor Spaces//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​Stone duality is a correspondence between Boolean algebras (BAs) and Boolean/​Stone topological spaces. ​ Dualizing the free BA $\textbf{F}(S)$ on set $S$ yields a product space $2^S$, where $2=\{0,1\}$ is discrete. ​ We call $2^S$ a generalized binary Cantor space (GCS$_2$), and similarly define the spaces GCS$_n$ with $n\ge 2$.  This talk introduces Stone duality and then answers the question ``what is dual to the class of GCS'​s?''​+   * **November 12**\\ <​html>​ <span style="​color:​blue;​font-size:​120%">​Dikran Karagueuzian ​</​span></​html>​(Binghamton University) ​\\ **//Title//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​Abstract
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- +   * **November 19**\\ <​html>​ <span style="​color:​blue;​font-size:​120%">​Zach Costanzo ​</​span></​html>​(Binghamton University) ​\\ **//​Title//​** \\    \\  <WRAP center box 90%> **//​Abstract//​**:​ Abstract
-   * **April 16**\\  <​html>​ <span style="​color:​blue;​font-size:​120%">​Speaker</​span></​html>​ \\      **//​Title ​of Talk//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​Text of Abstract+
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-   * **April 23**\\  <​html>​ <span style="​color:​blue;​font-size:​120%">​Joseph Cyr (Binghamton University)</​span></​html>​ \\      **//​Title ​of Talk//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​Text of Abstract+   * **November 26**\\ <​html>​ <span style="​color:​blue;​font-size:​120%">​Speaker ​</​span></​html>​(University) ​\\ **//​Title//​** \\    \\  <WRAP center box 90%> **//​Abstract//​**:​ Abstract
 </​WRAP>​ </​WRAP>​
-   * **April 30**\\  <​html>​ <span style="​color:​blue;​font-size:​120%">​Dikran Karagueuzian (Binghamton University)</​span></​html>​ \\      **//​Title ​of Talk//** \\    \\  <WRAP center box 90%> **//​Abstract//​**:​ Text of Abstract +   * **December 3 **\\ <​html>​ <span style="​color:​blue;​font-size:​120%">​Speaker ​</​span></​html>​(University) ​\\ **//​Title//​** \\    \\  <WRAP center box 90%> **//​Abstract//​**:​ Abstract
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-   * **May 7**\\  <​html>​ <span style="​color:​blue;​font-size:​120%">​Joshua Carey</​span></​html>​ \\      **//​(Candidacy Exam Part 1)//** \\    \\  <WRAP center box 90%> **//​Abstract//​**: ​Text of Abstract+
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   * [[seminars:​alge:​alge-fall2016]]  ​   * [[seminars:​alge:​alge-fall2016]]  ​
   * [[seminars:​alge:​alge-Spring2017|Spring 2017]]   * [[seminars:​alge:​alge-Spring2017|Spring 2017]]
-  * [[seminars:​alge:​alge-Fall2017|Fall 2017]]+  * [[seminars:​alge:​alge-fall2017]]
   * [[seminars:​alge:​alge-Spring2018|Spring 2018]]   * [[seminars:​alge:​alge-Spring2018|Spring 2018]]
-  * [[seminars:​alge:​alge-Fall2017|Fall 2018]] 
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seminars/alge.1553573468.txt · Last modified: 2019/03/26 00:11 by alex