CUNY Graduate Center RSS Feedshttp://www.gc.cuny.eduCopyright 2016 CUNY Graduate Center. All rights reserved.The bulk-boundary principle for topological insulators<p>Event Date: 10/21/2016 4:15:00 PM</p><p>Speaker:</p>
<p>Prof. Emil Prodan (Yeshiva University)</p>
<p>Abstract:</p>
<p>The bulk-boundary principle refers to remarkable<br />
property of topological insulators of supporting edge<br />
quantum modes which resist the phenomenon of An-<br />
derson localization. As the words suggest, the edge<br />
physics is determined entirely by the bulk physics. One<br />
way to understand this, is to formulate the problem in<br />
terms of simple operator algebras and to study their<br />
K-theories. The goal of my seminar is to exemplify<br />
how bulk-boundary principle follow from such analy-<br />
sis, mainly following the exposition from [1].<br />
[1] E. Prodan and H. Schulz-Baldes, Bulk and Bound-<br />
ary Invariants for Complex Topological Insulators: From<br />
K-Theory to Physics, (Mathematical Physics Studies,<br />
Springer, 2016)<br />
</p>
http://www.gc.cuny.edu/News/Calendar/Detail?id=37728http://wfs.gc.cuny.edu/myarmolinksy/friday_seminar.html1_010/21/20164:15 PM10/21/20165:30 PM365 Fifth AvenueThe Graduate CenterNot ApplicableFreeThis event is part of the weekly 'Math Seminars' offered by the Ph.D. Program in Mathematics at the Graduate Center of CUNY. They reflect the broad range of research interests of the Program.Mathematical Physics, Fourier Analysis37436Ricci Flow and non-negative curvature on four-dimensional cohomogeneity one manifolds<p>Event Date: 10/25/2016 2:45:00 PM</p><p>Speaker:</p>
<p>Anusha Krishnan (University of Pennsylvania)<br />
</p>
<p>Abstract:<br />
<span style="font-size:11.0pt;line-height:107%;
font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:
Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi;
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA">We show that $S^4$, $S^2\times S^2$, $\C P^2$ and $\C P^2 \# \overline{\C P^2}$ admit metrics of non-negative (sectional) curvature which under the Ricci flow immediately acquire some negatively curved two-planes. Although this was previously known for compact manifolds of dimension greater than five and for non-compact manifolds, these are the first compact four-dimensional examples showing such behaviour. Our proof makes use of the fact that these four-manifolds $M$ admit cohomogeneity one actions, i.e. an isometric action by a Lie group $G$ such that the orbit space $M/G$ is one-dimensional. This talk is based on joint work with Renato G. Bettiol.</span></p>
http://www.gc.cuny.edu/News/Calendar/Detail?id=37729http://www.sci.ccny.cuny.edu/~bsantoro/GCSeminar.html5_210/25/20162:45 PM10/25/20164:00 PM365 Fifth AvenueThe Graduate Center3212FreeThis event is part of the weekly 'Math Seminars' offered by the Ph.D. Program in Mathematics at the Graduate Center of CUNY. They reflect the broad range of research interests of the Program.CUNY Geometric Analysis Seminar37437Twisted Trace Formula: History, Proof and Applications<p>Event Date: 10/27/2016 4:00:00 PM</p><p align="LEFT"><font face="CMR10" size="5"><font face="CMR10" size="5">The twisted version of the Arthur-Selberg Trace Formula </font></font><font face="CMR10" size="5"><font face="CMR10" size="5">together with its stabilization, is the main technical tool for Base Change</font></font></p>
<p align="LEFT"><font face="CMR10" size="5"><font face="CMR10" size="5">and many more recent advances by J. Arthur and others on cases of </font></font><font face="CMR10" size="5"><font face="CMR10" size="5">Langlands functoriality. After a brief historical survey we shall explain </font></font><font face="CMR10" size="5"><font face="CMR10" size="5">some of the main steps in the proof of the Twisted Trace Formula itself </font></font><font face="CMR10" size="5"><font face="CMR10" size="5">and its stabilization.</font></font></p>
http://www.gc.cuny.edu/News/Calendar/Detail?id=37730http://www.math.columbia.edu/~goldfeld/ScheduleJointNTS27.html5_210/27/20164:00 PM10/27/20167:00 PMColumbia UniversityNot ApplicableFreeThis event is part of the weekly 'Math Seminars' offered by the Ph.D. Program in Mathematics at the Graduate Center of CUNY. They reflect the broad range of research interests of the Program.JOINT COLUMBIA-CUNY-NYU NUMBER THEORY SEMINAR37438Divergence of CAT(0) Cube Complexes and Right-Angled Coxeter Groups <p>Event Date: 10/25/2016 4:15:00 PM</p>Speaker: Ivan Levcovitz (CUNY)<br />
<br />
Abstract: The divergence function of a metric space, a quasi-isometry invariant, roughly measures the rate which pairs of geodesic rays stray apart. We will present new results regarding divergence functions of CAT(0) cube complexes. Right-angled Coxeter groups, in particular, exhibit a rich spectrum of possible divergence functions. The talk will give special focus to applications of our results to these groups. Applications to the theory of random right-angled Coxeter groups will also be briefly discussed.http://www.gc.cuny.edu/News/Calendar/Detail?id=37731http://comet.lehman.cuny.edu/behrstock/seminar/5_210/25/20164:15 PM10/25/20166:15 PM365 Fifth AvenueThe Graduate Center3212FreeThis event is part of the weekly 'Math Seminars' offered by the Ph.D. Program in Mathematics at the Graduate Center of CUNY. They reflect the broad range of research interests of the Program.CUNY Geometry and Topology Seminar37439Two-dimensional Blaschke Products: Degree Growth and Ergodic Consequences<p>Event Date: 10/28/2016 2:00:00 PM</p><p>Speaker:</p>
<h4><font face="Garamond" size="3">Enrique Pujals (IMPA and the Graduate Center of CUNY) </font></h4>
<p><br />
Abstract:<br />
<font face="Garamond" size="3">For dominant rational maps of compact, complex, Kahler manifolds there is a conjecture specifying the expected ergodic properties of the map depending on the relationship between the rates of growth for certain degrees under iteration of the map. In the present talk, we will discuss the case of two-dimensional Blaschke products, observing that they fit naturally within this conjecture, having examples from each of the three cases that the conjecture gives for maps of a surface.<br />
The results to be discussed are included in different works with Mike Shub and Roland Roeder. </font></p>
<p> </p>
http://www.gc.cuny.edu/News/Calendar/Detail?id=37827http://qcpages.qc.cuny.edu/~zakeri/seminar.html1_010/28/20162:00 PM10/28/20164:00 PM365 Fifth AvenueThe Graduate Center5417FreeThis event is part of the weekly 'Math Seminars' offered by the Ph.D. Program in Mathematics at the Graduate Center of CUNY. They reflect the broad range of research interests of the Program.Complex Analysis and Dynamics Seminar 37535Information Inequalities, Entropy Regions, and Groups<p>Event Date: 11/4/2016 2:30:00 PM</p><p>Speaker:</p>
<p>Nigel Boston (University of Wisconsin, Madison)</p>
<p>Abstract:</p>
<p>Entropy regions are fundamental but poorly understood objects, central to computing network coding capacities, but also describable purely in terms of groups. Nan and I have used group theory to shed light on these mysterious regions.</p>
http://www.gc.cuny.edu/News/Calendar/Detail?id=37828http://www.sci.ccny.cuny.edu/~shpil/algcryp.html1_011/04/20162:30 PM11/18/20163:30 PM365 Fifth AvenueThe Graduate Center3307FreeThis event is part of the weekly 'Math Seminars' offered by the Ph.D. Program in Mathematics at the Graduate Center of CUNY. They reflect the broad range of research interests of the Program.Algebra and Cryptography Seminar37536Non-Abelian Cohen-Lenstra Heuristics<p>Event Date: 11/3/2016 4:00:00 PM</p><p>**NOTE: <i><big><small style="color: rgb(0,
0, 0);"><small>The seminar will have a special RTG talk at 4:00 P.M. every Thursday when the seminar meets. The RTG talk will be aimed at graduate students and post-docs; regular faculty are requested not to attend. </small></small></big></i></p>
<p>RTG SEMINAR: 4:00-4:45</p>
<p>TEA: 5:00-5:30</p>
<p>TALK: 5:30-7:00</p>
<p>Speaker:</p>
<p>Nigel Boston (University of Wisconsin)</p>
<p>Abstract:<br />
<span style="font-size:11.0pt;line-height:107%;
font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:
Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi;
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA">In<span style="mso-spacerun:yes"> </span>1983,<span style="mso-spacerun:yes"> </span>Cohen<span style="mso-spacerun:yes"> </span>and<span style="mso-spacerun:yes"> </span>Lenstra<span style="mso-spacerun:yes"> </span>conjectured<span style="mso-spacerun:yes"> </span>the<span style="mso-spacerun:yes"> </span>distribution<span style="mso-spacerun:yes"> </span>of p-class groups of imaginary quadratic<span style="mso-spacerun:yes"> </span>fields (p odd).<span style="mso-spacerun:yes"> </span>These groups are the abelianizations<span style="mso-spacerun:yes"> </span>of p-class<span style="mso-spacerun:yes"> </span>tower<span style="mso-spacerun:yes"> </span>groups,<span style="mso-spacerun:yes"> </span>whose<span style="mso-spacerun:yes"> </span>distribution<span style="mso-spacerun:yes"> </span>Bush,<span style="mso-spacerun:yes"> </span>Hajir, and I recently conjectured.<span style="mso-spacerun:yes"> </span>Wood and I then computed the moments of this distribution and proved some function<span style="mso-spacerun:yes"> </span>field analogues.</span></p>
http://www.gc.cuny.edu/News/Calendar/Detail?id=37829http://www.math.columbia.edu/~goldfeld/ScheduleJointNTS27.html5_211/03/20164:00 PM11/03/20162:24 PM365 Fifth AvenueThe Graduate Center4102: Science CenterFreeThis event is part of the weekly 'Math Seminars' offered by the Ph.D. Program in Mathematics at the Graduate Center of CUNY. They reflect the broad range of research interests of the Program.New York Joint Columbia-CUNY-NYU Number Theory Seminar37537Learnability thesis, FM-representability and Turing Ideals<p>Event Date: 10/28/2016 2:00:00 PM</p><p>Speaker:<br />
Michał Tomasz Godziszewski</p>
<p>Abstract:</p>
<p>We consider the notion of the so-called intuitive learnability and its relation to the so-called intuitive computability. We briefly present and discuss Church’s Thesis in the context of the notion of learnability. A set is intuitively learnable if there is a (possibly infinite) intuitive procedure that for each input produces a finite sequence of yeses and nos such that the last answer in the sequence is correct. We further formulate the Learnability Thesis which states that the notion of intuitive learnability is equivalent to the notion of algorithmic learnability. The claim is analogous to Church’s Thesis. Afterwards we analyse the argument for Church’s Thesis presented by M. Mostowski (employing the concept of FM-representability which is equivalent to Turing-reducibility to 0′ or to being Delta^0_2. The argument goes in unusual lines – by giving a model of potential infinity, the so-called FM-domains, which are inifnite sequences of growing finite models, separating knowable (intuitively computable) sets from FM-representable (algorithmically learnable) ones via the so-called testing formulae and showing that knowable sets are exactly recursive. We indicate which assumptions of the Mostowski’s argument (concerning recursive enumeration of the finite models being elements of an FM-domain) implicitely include that Church’s Thesis holds. The impossibility of this kind of argument is strengthened by showing that the Learnability Thesis does not imply Church’s Thesis. Specifically, we show a natural interpretation of intuitive computability – containing a low set – under which intuitively learnable sets are exactly algorithmically learnable but intuitively computable sets form a proper superset of recursive sets. Last, using the Sacks Density Theorem, we show that there is a continuum of Turing ideals of low sets satisfying our assumptions. Therefore, if we admit certain non-recursive but intuitively computable relations (namely: some low relations) we are able to consider expanded FM-domains and there are continuum many of such. On the other hand, relations FM-representable in such FM-dommains are still Delta^0_2. The general conclusion is that justifying Church’s Thesis solely on the grounds of procedures recursive in the limit is by far insufficient.</p>
<div class="tag-list"> </div>
http://www.gc.cuny.edu/News/Calendar/Detail?id=37830http://nylogic.org/workshop5_210/28/20162:00 PM10/28/20163:45 PM365 Fifth AvenueThe Graduate Center6417FreeThis event is part of the weekly 'Math Seminars' offered by the Ph.D. Program in Mathematics at the Graduate Center of CUNY. They reflect the broad range of research interests of the Program.CUNY Logic Workshop37538Modular permutation invariants and quotients of spheres.<p>Event Date: 11/4/2016 4:15:00 PM</p><p>Speaker:<br />
<span style="font-size:11.0pt;line-height:107%;
font-family:"Calibri",sans-serif;mso-fareast-font-family:Calibri;mso-fareast-theme-font:
minor-latin;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi;
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA">Modular permutation invariants and quotients of spheres.</span><br />
<br />
Abstract:</p>
<p><span style="font-size:11.0pt;line-height:107%;
font-family:"Calibri",sans-serif;mso-fareast-font-family:Calibri;mso-fareast-theme-font:
minor-latin;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi;
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA">An important goal in the invariant theory of finite groups is to get information on the homological complexity of invariant rings when the characteristic of the coefficient field divides the group order ("the modular case"). This is irrelevant in the nonmodular case because such invariant rings are always Cohen-Macaulay, i.e. "homologically as simple as possible". This was proven over 40 years ago, but in the modular case even the question of when invariant rings are C-M is very far from settled. We apply work of Garsia and Stanton from the 80s to connect this question for permutation groups to the topology of a cell complex that is the quotient of a sphere by the group. Then we apply recent work of Christian Lange on sphere quotients to give a sufficient criterion for the invariant ring to be C-M over every ground field.</span></p>
<p> </p>
http://www.gc.cuny.edu/News/Calendar/Detail?id=378325_211/04/20164:15 PM11/04/20165:15 PM365 Fifth AvenueThe Graduate Center6417FreeThis event is part of the weekly 'Math Seminars' offered by the Ph.D. Program in Mathematics at the Graduate Center of CUNY. They reflect the broad range of research interests of the Program.
Commutative Algebra & Algebraic Geometry Seminar 37540On the real Jacobian conjecture <p>Event Date: 10/21/2016 4:15:00 PM</p><p>Full title: On the real Jacobian conjecture and its connections with the Hamiltonian differential systems</p>
<p>Speaker:</p>
<p>Malgorzata Marciniak, LaGuardia Community College<br />
</p>
<p>Abstract:</p>
<p>This talk will be a survey of the history of the real Jacobian conjecture. Originally formulated in 1939 by Keller for an arbitrary field, has two versions for real numbers. Given topological motivations, S. Pinchuk proved in 1994 that its strong version cannot be affirmative. Recently F. Brown, J. Gine and J. Llibre found a necessary and sufficient condition on the real polynomial map to have a globally defined polynomial inverse. Their proof is motivated by results by Sabatini from 1998 about isochronous Hamiltonian centers.<br />
</p>
http://www.gc.cuny.edu/News/Calendar/Detail?id=37833http://websupport1.citytech.cuny.edu/faculty/Selhitti/index_files/Page350.htm5_210/21/20164:15 PM10/21/20165:15 PM365 Fifth AvenueThe Graduate Center6417FreeThis event is part of the weekly 'Math Seminars' offered by the Ph.D. Program in Mathematics at the Graduate Center of CUNY. They reflect the broad range of research interests of the Program.
Commutative Algebra & Algebraic Geometry Seminar37541