https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Ongay&feedformat=atomUW-Math Wiki - User contributions [en]2019-10-23T16:08:45ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Graduate_Logic_Seminar&diff=16029Graduate Logic Seminar2018-09-20T18:23:13Z<p>Ongay: </p>
<hr />
<div>The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.<br />
<br />
* '''When:''' Fridays, 3:30 PM - 4:30 PM (unless otherwise announced).<br />
* '''Where:''' Van Vleck B115 (unless otherwise announced).<br />
* '''Organizers:''' [https://www.math.wisc.edu/~schweber/ Noah Schweber]<br />
<br />
Talks schedule are arrange and decide at the beginning of each semester. If you would like to participate, please contact one of the organizers.<br />
<br />
== Fall 2018 ==<br />
<br />
=== September 7, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== September 14, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== September 21, ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 28, ===<br />
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Title:<br />
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Abstract:<br />
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=== October 5, ===<br />
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Title: <br />
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Abstract: <br />
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=== October 12, ===<br />
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Title: <br />
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Abstract:<br />
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=== October 19, ===<br />
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Title:<br />
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Abstract:<br />
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=== October 26, ===<br />
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Title:<br />
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Abstract:<br />
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=== November 2, ===<br />
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Title:<br />
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Abstract:<br />
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=== November 9, ===<br />
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Title:<br />
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Abstract:<br />
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=== November 16, ===<br />
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Title:<br />
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Abstract:<br />
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=== November 23, ===<br />
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Title:<br />
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Abstract:<br />
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=== November 30, ===<br />
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Title:<br />
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Abstract:<br />
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=== December 7, ===<br />
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Title:<br />
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Abstract:<br />
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=== December 14, ===<br />
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Title:<br />
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Abstract:<br />
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=== December 21, ===<br />
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Title:<br />
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Abstract:<br />
<br />
==Previous Years==<br />
<br />
The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semesters|here]].</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Logic_Seminar&diff=16028Graduate Logic Seminar2018-09-20T18:22:08Z<p>Ongay: </p>
<hr />
<div>The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.<br />
<br />
* '''When:''' Fridays, 3:30 PM - 4:30 PM (unless otherwise announced).<br />
* '''Where:''' Van Vleck B115 (unless otherwise announced).<br />
* '''Organizers:''' [https://www.math.wisc.edu/~schweber/ Noah Schweber]<br />
<br />
Talks schedule are arrange and decide at the beginning of each semester. If you would like to participate, please contact one of the organizers.<br />
<br />
== Fall 2018 ==<br />
<br />
=== September 7, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== September 14, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== September 21, [] ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 28, ===<br />
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Title:<br />
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Abstract:<br />
<br />
=== October 5, ===<br />
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Title: <br />
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Abstract: <br />
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=== October 12, [] ===<br />
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Title: <br />
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Abstract:<br />
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=== October 19, [] ===<br />
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Title:<br />
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Abstract:<br />
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=== October 26, [] ===<br />
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Title:<br />
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Abstract:<br />
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=== November 2, [] ===<br />
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Title:<br />
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Abstract:<br />
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=== November 9, [] ===<br />
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Title:<br />
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Abstract:<br />
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=== November 16, [] ===<br />
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Title:<br />
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Abstract:<br />
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=== November 23, [] ===<br />
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Title:<br />
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Abstract:<br />
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=== November 30, [] ===<br />
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Title:<br />
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Abstract:<br />
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=== December 7, [] ===<br />
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Title:<br />
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Abstract:<br />
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=== December 14, [] ===<br />
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Title:<br />
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Abstract:<br />
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=== December 21, [] ===<br />
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Title:<br />
<br />
Abstract:<br />
<br />
==Previous Years==<br />
<br />
The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semesters|here]].</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Logic_Seminar,_previous_semesters&diff=16027Graduate Logic Seminar, previous semesters2018-09-20T18:15:13Z<p>Ongay: /* Graduate Logic Seminar Historic record */</p>
<hr />
<div>This is an historic listing of the talks in the [[Graduate Logic Seminar]].<br />
<br />
== Spring 2018 ==<br />
<br />
=== January 29, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== February 5, [http://www.math.wisc.edu/~andrews/ Uri Andrews] ===<br />
<br />
Title: Building Models of Strongly Minimal Theories - Part 1<br />
<br />
Abstract: Since I'm talking in the Tuesday seminar as well, I'll use the Monday seminar talk to do some background on the topic and some<br />
lemmas that will go into the proofs in Tuesday's talk. There will be (I hope) some theorems of interest to see on both days, and both on<br />
the general topic of answering the following question: What do you need to know about a strongly minimal theory in order to compute<br />
copies of all of its countable models. I'll start with a definition for strongly minimal theories and build up from there.<br />
<br />
=== February 12, James Hanson ===<br />
<br />
Title: Finding Definable Sets in Continuous Logic<br />
<br />
Abstract: In order to be useful the notion of a 'definable set' in continuous logic is stricter than a naive comparison to discrete logic<br />
would suggest. As a consequence, even in relatively tame theories there can be very few definable sets. For example, there is a<br />
superstable theory with no non-trivial definable sets. As we'll see, however, there are many definable sets in omega-stable,<br />
omega-categorical, and other small theories.<br />
<br />
=== February 19, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: Proper forcing<br />
<br />
Abstract: Although a given forcing notion may have nice properties on its own, those properties might vanish when we apply it repeatedly.<br />
Early preservation results (that is, theorems saying that the iteration of forcings with a nice property retains that nice property)<br />
were fairly limited, and things really got off the ground with Shelah's invention of "proper forcing." Roughly speaking, a forcing is<br />
proper if it can be approximated by elementary submodels of the universe in a particularly nice way. I'll define proper forcing and<br />
sketch some applications. <br />
<br />
=== February 26, Patrick Nicodemus ===<br />
<br />
Title: A survey of computable and constructive mathematics in economic history<br />
<br />
=== March 5, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===<br />
<br />
Title: Convexly Orderable Groups <br />
<br />
=== March 12, [https://math.nd.edu/people/visiting-faculty/daniel-turetsky/ Dan Turetsky] (University of Notre Dame) ===<br />
<br />
Title: Structural Jump<br />
<br />
=== March 19, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===<br />
<br />
Title: Networks and degrees of points in non-second countable spaces<br />
<br />
=== April 2, Wil Cocke ===<br />
<br />
Title: Characterizing Finite Nilpotent Groups via Word Maps<br />
<br />
Abstract: In this talk, we will examine a novel characterization of finite nilpotent groups using the probability distributions induced by word maps. In particular we show that a finite group is nilpotent if and only if every surjective word map has fibers of uniform size.<br />
<br />
=== April 9, Tejas Bhojraj ===<br />
<br />
Title: Quantum Randomness<br />
<br />
Abstract: I will read the paper by Nies and Scholz where they define a notion of algorithmic randomness for infinite sequences of quantum bits (qubits). This talk will cover the basic notions of quantum randomness on which my talk on Tuesday will be based. <br />
<br />
=== April 16, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===<br />
<br />
Title: What can we say about sets made by the union of Turing equivalence classes?<br />
<br />
Abstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type 'the rationals' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes?<br />
<br />
This topic hasn't been deeply studied. In this talk I will focus principally on famous order types and answer whether they can be achieved or not. Furthermore, I will explain some possible connections with the automorphism problem of the Turing degrees.<br />
<br />
This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation.(hopefully).<br />
<br />
=== April 23, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] (Thesis Defense) Start 3:45 Room B231===<br />
<br />
Title: Cototal enumeration degrees and their applications to effective mathematics <br />
<br />
Abstract: The enumeration degrees measure the relative computational difficulty of enumerating sets of natural numbers. Unlike the Turing degrees, the enumeration degrees of a set and its complement need not be comparable. A set is total if it is enumeration above its complement. Taken together, the enumeration degrees of total sets form an embedded copy of the Turing degrees within the enumeration degrees. A set of natural numbers is cototal if it is enumeration reducible to its complement. Surprisingly, the degrees of cototal sets, the cototal degrees, form an intermediate structure strictly between the total degrees and the enumeration degrees. <br />
<br />
Jeandel observed that cototal sets appear in a wide class of structures: as the word problems of simple groups, as the languages of minimal subshifts, and more generally as the maximal points of any c.e. quasivariety. In the case of minimal subshifts, the enumeration degree of the subshift's language determines the subshift's Turing degree spectrum: the collection of Turing degrees obtained by the points of the subshift. We prove that cototality precisely characterizes the Turing degree spectra of minimal subshifts: the degree spectra of nontrivial minimal subshifts are precisely the cototal enumeration cones. On the way to this result, we will give several other characterizations of the cototal degrees, including as the degrees of maximal anti-chain complements on <math>\omega^{<\omega}</math>, and as the degrees of enumeration-pointed trees on <math>2^{<\omega}</math>, and we will remark on some additional applications of these characterizations.<br />
<br />
=== April 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde]===<br />
<br />
Title: Definibility of the Frobenius orbits and an application to sets of rational distances.<br />
<br />
Abstract: In this talk I'll present a paper by Hector Pastén. We will talk about how having a formula that identify a Frobenius orbits can help you show an analogue case of Hilbert's tenth problem (the one asking for an algorithm that tells you if a diophantine equation is solvable or not).<br />
<br />
Finally, if time permits, we will do an application that solves the existence of a dense set in the plane with rational distances, assuming some form of the ABC conjecture. This last question was propose by Erdös and Ulam.<br />
<br />
== Fall 2017 ==<br />
<br />
=== September 11, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== September 18, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: The Kunen inconsistency<br />
<br />
Abstract: While early large cardinal axioms were usually defined combinatorially - e.g., cardinals satisfying a version of Ramsey's<br />
theorem - later focus shifted to model-theoretic definitions, specifically definitions in terms of elementary embeddings of the<br />
whole universe of sets. At the lowest level, a measurable cardinal is one which is the least cardinal moved (= critical point) by a<br />
nontrivial elementary embedding from V into some inner model M.<br />
<br />
There are several variations on this theme yielding stronger and stronger large cardinal notions; one of the most important is the<br />
inclusion of *correctness properties* of the target model M. The strongest such correctness property is total correctness: M=V. The<br />
critical point of an elementary embedding from V to V is called a *Reinhardt cardinal*. Shortly after their introduction in Reinhardt's<br />
thesis, however, the existence of a Reinhardt cardinal was shown to be inconsistent with ZFC.<br />
<br />
I'll present this argument, and talk a bit about the role of choice. <br />
<br />
=== September 25, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: Hindman's theorem via ultrafilters<br />
<br />
Abstract: Hindman's theorem is a Ramsey-type theorem in additive combinatorics: if we color the natural numbers with two colors, there is an infinite set such that any *finite sum* from that set has the same color as any other finite sum. There are (to my knowledge) two proofs of Hindman's theorem: one of them is a complicated mess of combinatorics, and the other consists of cheating wildly. We'll do.<br />
<br />
=== October 2, James Hanson ===<br />
<br />
Title: The Gromov-Hausdorff metric on type space in continuous logic<br />
<br />
Abstract: The Gromov-Hausdorff metric is a notion of the 'distance' between two metric spaces. Although it is typically studied in the context of compact or locally compact metric spaces, the definition is sensible even when applied to non-compact metric spaces, but in that context it is only a pseudo-metric: there are non-isomorphic metric spaces with Gromov-Hausdorff distance 0. This gives rise to an equivalence relation that is slightly coarser than isomorphism. There are continuous first-order theories which are categorical with regards to this equivalence relation while failing to be isometrically categorical, so it is natural to look for analogs of the Ryll-Nardzewski theorem and Morley's theorem, but before we can do any of that, it'll be necessary to learn about the "topometric" structure induced on type space by the Gromov-Hausdorff metric.<br />
<br />
=== October 9, James Hanson ===<br />
<br />
Title: Morley rank and stability in continuous logic<br />
<br />
Abstract: There are various ways of counting the 'size' of subsets of metric spaces. Using these we can do a kind of Cantor-Bendixson analysis on type spaces in continuous first-order theories, and thereby define a notion of Morley rank. More directly we can define<br />
> the 'correct' notion of stability in the continuous setting. There are also natural Gromov-Hausdorff (GH) analogs of these notions. With this we'll prove that inseparably categorical theories have atomic models over arbitrary sets, which is an important step in the proof of Morley's theorem in this setting. The same proof with essentially cosmetic changes gives that inseparably GH-categorical theories have 'GH-atomic' models over arbitrary sets, but GH-atomic models fail to be GH-unique in general.<br />
<br />
=== October 23, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===<br />
<br />
Title: Boxy sets in ordered convexly-orderable structures.<br />
<br />
=== October 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===<br />
<br />
Title: Dancing SCCA and other Coloring Axioms<br />
<br />
Abstract: In this talk I will talk about some axioms that are closely related to SOCA (Semi Open Coloring Axiom), being the main protagonist SCCA (Semi Clopen Coloring Axiom). I will give a motivation on the statements of both axioms, a little historic perspective and showing that both axioms coincide for separable Baire spaces. This is a work in progress, so I will share some open questions that I'm happy to discuss.<br />
<br />
=== November 6, Wil Cocke ===<br />
<br />
Title: Two new characterizations of nilpotent groups<br />
<br />
Abstract: We will give two new characterizations of finite nilpotent groups. One using information about the order of products of elements of prime order and the other using the induced probability distribution from word maps.<br />
<br />
Or...<br />
<br />
Title: Centralizing Propagating Properties of Groups<br />
<br />
Abstract: We will examine some sentences known to have finite spectrum when conjoined with the theory of groups. Hopefully we will be able to find new examples. <br />
<br />
=== November 13, [https://www.math.wisc.edu/~lempp/ Steffen Lempp] ===<br />
<br />
Title: The computational complexity of properties of finitely presented groups<br />
<br />
Abstract: I will survey index set complexity results on finitely presented groups.<br />
<br />
=== November 20, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===<br />
<br />
Title: Strong Difference Randomness<br />
<br />
Abstract: The difference randoms were introduced by Franklin and Ng to characterize the incomplete Martin-Löf randoms. More recently, Bienvenu and Porter introduced the strong difference randoms, obtained by imposing the Solovay condition over the class of difference tests. I will give a Demuth test characterization of the strong difference randoms, along with a lowness characterization of them among the Martin-Löf randoms. <br />
<br />
=== December 4, Tejas Bhojraj ===<br />
<br />
Title: Quantum Algorithmic Randomness<br />
<br />
Abstract: I will discuss the recent paper by Nies and Scholz where they define quantum Martin-Lof randomness (q-MLR) for infinite sequences of qubits. If time permits, I will introduce the notion of quantum Solovay randomness and show that it is equivalent to q-MLR in some special cases.<br />
<br />
=== December 11, Grigory Terlov ===<br />
<br />
Title: The Logic of Erdős–Rényi Graphs</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Logic_Seminar&diff=16026Graduate Logic Seminar2018-09-20T18:13:56Z<p>Ongay: /* Previous Years */</p>
<hr />
<div>The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.<br />
<br />
* '''When:''' Fridays, 3:30 PM - 4:30 PM (unless otherwise announced).<br />
* '''Where:''' Van Vleck B115 (unless otherwise announced).<br />
* '''Organizers:''' [https://www.math.wisc.edu/~schweber/ Noah Schweber]<br />
<br />
Talks schedule are arrange and decide at the beginning of each semester. If you would like to participate, please contact one of the organizers.<br />
<br />
== Spring 2018 ==<br />
<br />
=== January 29, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== February 5, [http://www.math.wisc.edu/~andrews/ Uri Andrews] ===<br />
<br />
Title: Building Models of Strongly Minimal Theories - Part 1<br />
<br />
Abstract: Since I'm talking in the Tuesday seminar as well, I'll use the Monday seminar talk to do some background on the topic and some<br />
lemmas that will go into the proofs in Tuesday's talk. There will be (I hope) some theorems of interest to see on both days, and both on<br />
the general topic of answering the following question: What do you need to know about a strongly minimal theory in order to compute<br />
copies of all of its countable models. I'll start with a definition for strongly minimal theories and build up from there.<br />
<br />
=== February 12, James Hanson ===<br />
<br />
Title: Finding Definable Sets in Continuous Logic<br />
<br />
Abstract: In order to be useful the notion of a 'definable set' in continuous logic is stricter than a naive comparison to discrete logic<br />
would suggest. As a consequence, even in relatively tame theories there can be very few definable sets. For example, there is a<br />
superstable theory with no non-trivial definable sets. As we'll see, however, there are many definable sets in omega-stable,<br />
omega-categorical, and other small theories.<br />
<br />
=== February 19, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: Proper forcing<br />
<br />
Abstract: Although a given forcing notion may have nice properties on its own, those properties might vanish when we apply it repeatedly.<br />
Early preservation results (that is, theorems saying that the iteration of forcings with a nice property retains that nice property)<br />
were fairly limited, and things really got off the ground with Shelah's invention of "proper forcing." Roughly speaking, a forcing is<br />
proper if it can be approximated by elementary submodels of the universe in a particularly nice way. I'll define proper forcing and<br />
sketch some applications. <br />
<br />
=== February 26, Patrick Nicodemus ===<br />
<br />
Title: A survey of computable and constructive mathematics in economic history<br />
<br />
=== March 5, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===<br />
<br />
Title: Convexly Orderable Groups <br />
<br />
=== March 12, [https://math.nd.edu/people/visiting-faculty/daniel-turetsky/ Dan Turetsky] (University of Notre Dame) ===<br />
<br />
Title: Structural Jump<br />
<br />
=== March 19, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===<br />
<br />
Title: Networks and degrees of points in non-second countable spaces<br />
<br />
=== April 2, Wil Cocke ===<br />
<br />
Title: Characterizing Finite Nilpotent Groups via Word Maps<br />
<br />
Abstract: In this talk, we will examine a novel characterization of finite nilpotent groups using the probability distributions induced by word maps. In particular we show that a finite group is nilpotent if and only if every surjective word map has fibers of uniform size.<br />
<br />
=== April 9, Tejas Bhojraj ===<br />
<br />
Title: Quantum Randomness<br />
<br />
Abstract: I will read the paper by Nies and Scholz where they define a notion of algorithmic randomness for infinite sequences of quantum bits (qubits). This talk will cover the basic notions of quantum randomness on which my talk on Tuesday will be based. <br />
<br />
=== April 16, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===<br />
<br />
Title: What can we say about sets made by the union of Turing equivalence classes?<br />
<br />
Abstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type 'the rationals' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes?<br />
<br />
This topic hasn't been deeply studied. In this talk I will focus principally on famous order types and answer whether they can be achieved or not. Furthermore, I will explain some possible connections with the automorphism problem of the Turing degrees.<br />
<br />
This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation.(hopefully).<br />
<br />
=== April 23, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] (Thesis Defense) Start 3:45 Room B231===<br />
<br />
Title: Cototal enumeration degrees and their applications to effective mathematics <br />
<br />
Abstract: The enumeration degrees measure the relative computational difficulty of enumerating sets of natural numbers. Unlike the Turing degrees, the enumeration degrees of a set and its complement need not be comparable. A set is total if it is enumeration above its complement. Taken together, the enumeration degrees of total sets form an embedded copy of the Turing degrees within the enumeration degrees. A set of natural numbers is cototal if it is enumeration reducible to its complement. Surprisingly, the degrees of cototal sets, the cototal degrees, form an intermediate structure strictly between the total degrees and the enumeration degrees. <br />
<br />
Jeandel observed that cototal sets appear in a wide class of structures: as the word problems of simple groups, as the languages of minimal subshifts, and more generally as the maximal points of any c.e. quasivariety. In the case of minimal subshifts, the enumeration degree of the subshift's language determines the subshift's Turing degree spectrum: the collection of Turing degrees obtained by the points of the subshift. We prove that cototality precisely characterizes the Turing degree spectra of minimal subshifts: the degree spectra of nontrivial minimal subshifts are precisely the cototal enumeration cones. On the way to this result, we will give several other characterizations of the cototal degrees, including as the degrees of maximal anti-chain complements on <math>\omega^{<\omega}</math>, and as the degrees of enumeration-pointed trees on <math>2^{<\omega}</math>, and we will remark on some additional applications of these characterizations.<br />
<br />
=== April 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde]===<br />
<br />
Title: Definibility of the Frobenius orbits and an application to sets of rational distances.<br />
<br />
Abstract: In this talk I'll present a paper by Hector Pastén. We will talk about how having a formula that identify a Frobenius orbits can help you show an analogue case of Hilbert's tenth problem (the one asking for an algorithm that tells you if a diophantine equation is solvable or not).<br />
<br />
Finally, if time permits, we will do an application that solves the existence of a dense set in the plane with rational distances, assuming some form of the ABC conjecture. This last question was propose by Erdös and Ulam.<br />
<br />
== Fall 2017 ==<br />
<br />
=== September 11, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== September 18, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: The Kunen inconsistency<br />
<br />
Abstract: While early large cardinal axioms were usually defined combinatorially - e.g., cardinals satisfying a version of Ramsey's<br />
theorem - later focus shifted to model-theoretic definitions, specifically definitions in terms of elementary embeddings of the<br />
whole universe of sets. At the lowest level, a measurable cardinal is one which is the least cardinal moved (= critical point) by a<br />
nontrivial elementary embedding from V into some inner model M.<br />
<br />
There are several variations on this theme yielding stronger and stronger large cardinal notions; one of the most important is the<br />
inclusion of *correctness properties* of the target model M. The strongest such correctness property is total correctness: M=V. The<br />
critical point of an elementary embedding from V to V is called a *Reinhardt cardinal*. Shortly after their introduction in Reinhardt's<br />
thesis, however, the existence of a Reinhardt cardinal was shown to be inconsistent with ZFC.<br />
<br />
I'll present this argument, and talk a bit about the role of choice. <br />
<br />
=== September 25, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: Hindman's theorem via ultrafilters<br />
<br />
Abstract: Hindman's theorem is a Ramsey-type theorem in additive combinatorics: if we color the natural numbers with two colors, there is an infinite set such that any *finite sum* from that set has the same color as any other finite sum. There are (to my knowledge) two proofs of Hindman's theorem: one of them is a complicated mess of combinatorics, and the other consists of cheating wildly. We'll do.<br />
<br />
=== October 2, James Hanson ===<br />
<br />
Title: The Gromov-Hausdorff metric on type space in continuous logic<br />
<br />
Abstract: The Gromov-Hausdorff metric is a notion of the 'distance' between two metric spaces. Although it is typically studied in the context of compact or locally compact metric spaces, the definition is sensible even when applied to non-compact metric spaces, but in that context it is only a pseudo-metric: there are non-isomorphic metric spaces with Gromov-Hausdorff distance 0. This gives rise to an equivalence relation that is slightly coarser than isomorphism. There are continuous first-order theories which are categorical with regards to this equivalence relation while failing to be isometrically categorical, so it is natural to look for analogs of the Ryll-Nardzewski theorem and Morley's theorem, but before we can do any of that, it'll be necessary to learn about the "topometric" structure induced on type space by the Gromov-Hausdorff metric.<br />
<br />
=== October 9, James Hanson ===<br />
<br />
Title: Morley rank and stability in continuous logic<br />
<br />
Abstract: There are various ways of counting the 'size' of subsets of metric spaces. Using these we can do a kind of Cantor-Bendixson analysis on type spaces in continuous first-order theories, and thereby define a notion of Morley rank. More directly we can define<br />
> the 'correct' notion of stability in the continuous setting. There are also natural Gromov-Hausdorff (GH) analogs of these notions. With this we'll prove that inseparably categorical theories have atomic models over arbitrary sets, which is an important step in the proof of Morley's theorem in this setting. The same proof with essentially cosmetic changes gives that inseparably GH-categorical theories have 'GH-atomic' models over arbitrary sets, but GH-atomic models fail to be GH-unique in general.<br />
<br />
=== October 23, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===<br />
<br />
Title: Boxy sets in ordered convexly-orderable structures.<br />
<br />
=== October 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===<br />
<br />
Title: Dancing SCCA and other Coloring Axioms<br />
<br />
Abstract: In this talk I will talk about some axioms that are closely related to SOCA (Semi Open Coloring Axiom), being the main protagonist SCCA (Semi Clopen Coloring Axiom). I will give a motivation on the statements of both axioms, a little historic perspective and showing that both axioms coincide for separable Baire spaces. This is a work in progress, so I will share some open questions that I'm happy to discuss.<br />
<br />
=== November 6, Wil Cocke ===<br />
<br />
Title: Two new characterizations of nilpotent groups<br />
<br />
Abstract: We will give two new characterizations of finite nilpotent groups. One using information about the order of products of elements of prime order and the other using the induced probability distribution from word maps.<br />
<br />
Or...<br />
<br />
Title: Centralizing Propagating Properties of Groups<br />
<br />
Abstract: We will examine some sentences known to have finite spectrum when conjoined with the theory of groups. Hopefully we will be able to find new examples. <br />
<br />
=== November 13, [https://www.math.wisc.edu/~lempp/ Steffen Lempp] ===<br />
<br />
Title: The computational complexity of properties of finitely presented groups<br />
<br />
Abstract: I will survey index set complexity results on finitely presented groups.<br />
<br />
=== November 20, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===<br />
<br />
Title: Strong Difference Randomness<br />
<br />
Abstract: The difference randoms were introduced by Franklin and Ng to characterize the incomplete Martin-Löf randoms. More recently, Bienvenu and Porter introduced the strong difference randoms, obtained by imposing the Solovay condition over the class of difference tests. I will give a Demuth test characterization of the strong difference randoms, along with a lowness characterization of them among the Martin-Löf randoms. <br />
<br />
=== December 4, Tejas Bhojraj ===<br />
<br />
Title: Quantum Algorithmic Randomness<br />
<br />
Abstract: I will discuss the recent paper by Nies and Scholz where they define quantum Martin-Lof randomness (q-MLR) for infinite sequences of qubits. If time permits, I will introduce the notion of quantum Solovay randomness and show that it is equivalent to q-MLR in some special cases.<br />
<br />
=== December 11, Grigory Terlov ===<br />
<br />
Title: The Logic of Erdős–Rényi Graphs<br />
<br />
==Previous Years==<br />
<br />
The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semesters|here]].</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Logic_Graduate_Seminar,_previous_semesters&diff=16025Logic Graduate Seminar, previous semesters2018-09-20T18:12:52Z<p>Ongay: </p>
<hr />
<div>This is an historic listing of the talks in the [[Graduate Logic Seminar]].<br />
<br />
== Spring 2018 ==<br />
<br />
=== January 29, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== February 5, [http://www.math.wisc.edu/~andrews/ Uri Andrews] ===<br />
<br />
Title: Building Models of Strongly Minimal Theories - Part 1<br />
<br />
Abstract: Since I'm talking in the Tuesday seminar as well, I'll use the Monday seminar talk to do some background on the topic and some<br />
lemmas that will go into the proofs in Tuesday's talk. There will be (I hope) some theorems of interest to see on both days, and both on<br />
the general topic of answering the following question: What do you need to know about a strongly minimal theory in order to compute<br />
copies of all of its countable models. I'll start with a definition for strongly minimal theories and build up from there.<br />
<br />
=== February 12, James Hanson ===<br />
<br />
Title: Finding Definable Sets in Continuous Logic<br />
<br />
Abstract: In order to be useful the notion of a 'definable set' in continuous logic is stricter than a naive comparison to discrete logic<br />
would suggest. As a consequence, even in relatively tame theories there can be very few definable sets. For example, there is a<br />
superstable theory with no non-trivial definable sets. As we'll see, however, there are many definable sets in omega-stable,<br />
omega-categorical, and other small theories.<br />
<br />
=== February 19, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: Proper forcing<br />
<br />
Abstract: Although a given forcing notion may have nice properties on its own, those properties might vanish when we apply it repeatedly.<br />
Early preservation results (that is, theorems saying that the iteration of forcings with a nice property retains that nice property)<br />
were fairly limited, and things really got off the ground with Shelah's invention of "proper forcing." Roughly speaking, a forcing is<br />
proper if it can be approximated by elementary submodels of the universe in a particularly nice way. I'll define proper forcing and<br />
sketch some applications. <br />
<br />
=== February 26, Patrick Nicodemus ===<br />
<br />
Title: A survey of computable and constructive mathematics in economic history<br />
<br />
=== March 5, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===<br />
<br />
Title: Convexly Orderable Groups <br />
<br />
=== March 12, [https://math.nd.edu/people/visiting-faculty/daniel-turetsky/ Dan Turetsky] (University of Notre Dame) ===<br />
<br />
Title: Structural Jump<br />
<br />
=== March 19, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===<br />
<br />
Title: Networks and degrees of points in non-second countable spaces<br />
<br />
=== April 2, Wil Cocke ===<br />
<br />
Title: Characterizing Finite Nilpotent Groups via Word Maps<br />
<br />
Abstract: In this talk, we will examine a novel characterization of finite nilpotent groups using the probability distributions induced by word maps. In particular we show that a finite group is nilpotent if and only if every surjective word map has fibers of uniform size.<br />
<br />
=== April 9, Tejas Bhojraj ===<br />
<br />
Title: Quantum Randomness<br />
<br />
Abstract: I will read the paper by Nies and Scholz where they define a notion of algorithmic randomness for infinite sequences of quantum bits (qubits). This talk will cover the basic notions of quantum randomness on which my talk on Tuesday will be based. <br />
<br />
=== April 16, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===<br />
<br />
Title: What can we say about sets made by the union of Turing equivalence classes?<br />
<br />
Abstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type 'the rationals' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes?<br />
<br />
This topic hasn't been deeply studied. In this talk I will focus principally on famous order types and answer whether they can be achieved or not. Furthermore, I will explain some possible connections with the automorphism problem of the Turing degrees.<br />
<br />
This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation.(hopefully).<br />
<br />
=== April 23, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] (Thesis Defense) Start 3:45 Room B231===<br />
<br />
Title: Cototal enumeration degrees and their applications to effective mathematics <br />
<br />
Abstract: The enumeration degrees measure the relative computational difficulty of enumerating sets of natural numbers. Unlike the Turing degrees, the enumeration degrees of a set and its complement need not be comparable. A set is total if it is enumeration above its complement. Taken together, the enumeration degrees of total sets form an embedded copy of the Turing degrees within the enumeration degrees. A set of natural numbers is cototal if it is enumeration reducible to its complement. Surprisingly, the degrees of cototal sets, the cototal degrees, form an intermediate structure strictly between the total degrees and the enumeration degrees. <br />
<br />
Jeandel observed that cototal sets appear in a wide class of structures: as the word problems of simple groups, as the languages of minimal subshifts, and more generally as the maximal points of any c.e. quasivariety. In the case of minimal subshifts, the enumeration degree of the subshift's language determines the subshift's Turing degree spectrum: the collection of Turing degrees obtained by the points of the subshift. We prove that cototality precisely characterizes the Turing degree spectra of minimal subshifts: the degree spectra of nontrivial minimal subshifts are precisely the cototal enumeration cones. On the way to this result, we will give several other characterizations of the cototal degrees, including as the degrees of maximal anti-chain complements on <math>\omega^{<\omega}</math>, and as the degrees of enumeration-pointed trees on <math>2^{<\omega}</math>, and we will remark on some additional applications of these characterizations.<br />
<br />
=== April 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde]===<br />
<br />
Title: Definibility of the Frobenius orbits and an application to sets of rational distances.<br />
<br />
Abstract: In this talk I'll present a paper by Hector Pastén. We will talk about how having a formula that identify a Frobenius orbits can help you show an analogue case of Hilbert's tenth problem (the one asking for an algorithm that tells you if a diophantine equation is solvable or not).<br />
<br />
Finally, if time permits, we will do an application that solves the existence of a dense set in the plane with rational distances, assuming some form of the ABC conjecture. This last question was propose by Erdös and Ulam.<br />
<br />
== Fall 2017 ==<br />
<br />
=== September 11, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== September 18, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: The Kunen inconsistency<br />
<br />
Abstract: While early large cardinal axioms were usually defined combinatorially - e.g., cardinals satisfying a version of Ramsey's<br />
theorem - later focus shifted to model-theoretic definitions, specifically definitions in terms of elementary embeddings of the<br />
whole universe of sets. At the lowest level, a measurable cardinal is one which is the least cardinal moved (= critical point) by a<br />
nontrivial elementary embedding from V into some inner model M.<br />
<br />
There are several variations on this theme yielding stronger and stronger large cardinal notions; one of the most important is the<br />
inclusion of *correctness properties* of the target model M. The strongest such correctness property is total correctness: M=V. The<br />
critical point of an elementary embedding from V to V is called a *Reinhardt cardinal*. Shortly after their introduction in Reinhardt's<br />
thesis, however, the existence of a Reinhardt cardinal was shown to be inconsistent with ZFC.<br />
<br />
I'll present this argument, and talk a bit about the role of choice. <br />
<br />
=== September 25, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: Hindman's theorem via ultrafilters<br />
<br />
Abstract: Hindman's theorem is a Ramsey-type theorem in additive combinatorics: if we color the natural numbers with two colors, there is an infinite set such that any *finite sum* from that set has the same color as any other finite sum. There are (to my knowledge) two proofs of Hindman's theorem: one of them is a complicated mess of combinatorics, and the other consists of cheating wildly. We'll do.<br />
<br />
=== October 2, James Hanson ===<br />
<br />
Title: The Gromov-Hausdorff metric on type space in continuous logic<br />
<br />
Abstract: The Gromov-Hausdorff metric is a notion of the 'distance' between two metric spaces. Although it is typically studied in the context of compact or locally compact metric spaces, the definition is sensible even when applied to non-compact metric spaces, but in that context it is only a pseudo-metric: there are non-isomorphic metric spaces with Gromov-Hausdorff distance 0. This gives rise to an equivalence relation that is slightly coarser than isomorphism. There are continuous first-order theories which are categorical with regards to this equivalence relation while failing to be isometrically categorical, so it is natural to look for analogs of the Ryll-Nardzewski theorem and Morley's theorem, but before we can do any of that, it'll be necessary to learn about the "topometric" structure induced on type space by the Gromov-Hausdorff metric.<br />
<br />
=== October 9, James Hanson ===<br />
<br />
Title: Morley rank and stability in continuous logic<br />
<br />
Abstract: There are various ways of counting the 'size' of subsets of metric spaces. Using these we can do a kind of Cantor-Bendixson analysis on type spaces in continuous first-order theories, and thereby define a notion of Morley rank. More directly we can define<br />
> the 'correct' notion of stability in the continuous setting. There are also natural Gromov-Hausdorff (GH) analogs of these notions. With this we'll prove that inseparably categorical theories have atomic models over arbitrary sets, which is an important step in the proof of Morley's theorem in this setting. The same proof with essentially cosmetic changes gives that inseparably GH-categorical theories have 'GH-atomic' models over arbitrary sets, but GH-atomic models fail to be GH-unique in general.<br />
<br />
=== October 23, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===<br />
<br />
Title: Boxy sets in ordered convexly-orderable structures.<br />
<br />
=== October 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===<br />
<br />
Title: Dancing SCCA and other Coloring Axioms<br />
<br />
Abstract: In this talk I will talk about some axioms that are closely related to SOCA (Semi Open Coloring Axiom), being the main protagonist SCCA (Semi Clopen Coloring Axiom). I will give a motivation on the statements of both axioms, a little historic perspective and showing that both axioms coincide for separable Baire spaces. This is a work in progress, so I will share some open questions that I'm happy to discuss.<br />
<br />
=== November 6, Wil Cocke ===<br />
<br />
Title: Two new characterizations of nilpotent groups<br />
<br />
Abstract: We will give two new characterizations of finite nilpotent groups. One using information about the order of products of elements of prime order and the other using the induced probability distribution from word maps.<br />
<br />
Or...<br />
<br />
Title: Centralizing Propagating Properties of Groups<br />
<br />
Abstract: We will examine some sentences known to have finite spectrum when conjoined with the theory of groups. Hopefully we will be able to find new examples. <br />
<br />
=== November 13, [https://www.math.wisc.edu/~lempp/ Steffen Lempp] ===<br />
<br />
Title: The computational complexity of properties of finitely presented groups<br />
<br />
Abstract: I will survey index set complexity results on finitely presented groups.<br />
<br />
=== November 20, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===<br />
<br />
Title: Strong Difference Randomness<br />
<br />
Abstract: The difference randoms were introduced by Franklin and Ng to characterize the incomplete Martin-Löf randoms. More recently, Bienvenu and Porter introduced the strong difference randoms, obtained by imposing the Solovay condition over the class of difference tests. I will give a Demuth test characterization of the strong difference randoms, along with a lowness characterization of them among the Martin-Löf randoms. <br />
<br />
=== December 4, Tejas Bhojraj ===<br />
<br />
Title: Quantum Algorithmic Randomness<br />
<br />
Abstract: I will discuss the recent paper by Nies and Scholz where they define quantum Martin-Lof randomness (q-MLR) for infinite sequences of qubits. If time permits, I will introduce the notion of quantum Solovay randomness and show that it is equivalent to q-MLR in some special cases.<br />
<br />
=== December 11, Grigory Terlov ===<br />
<br />
Title: The Logic of Erdős–Rényi Graphs</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Logic_Graduate_Seminar,_previous_semesters&diff=16024Logic Graduate Seminar, previous semesters2018-09-20T18:12:03Z<p>Ongay: Logic Graduate Student Seminar Historic Record</p>
<hr />
<div>This is an historic listing of the talks in the [[Graduate Logic Student Seminar]].<br />
<br />
== Spring 2018 ==<br />
<br />
=== January 29, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== February 5, [http://www.math.wisc.edu/~andrews/ Uri Andrews] ===<br />
<br />
Title: Building Models of Strongly Minimal Theories - Part 1<br />
<br />
Abstract: Since I'm talking in the Tuesday seminar as well, I'll use the Monday seminar talk to do some background on the topic and some<br />
lemmas that will go into the proofs in Tuesday's talk. There will be (I hope) some theorems of interest to see on both days, and both on<br />
the general topic of answering the following question: What do you need to know about a strongly minimal theory in order to compute<br />
copies of all of its countable models. I'll start with a definition for strongly minimal theories and build up from there.<br />
<br />
=== February 12, James Hanson ===<br />
<br />
Title: Finding Definable Sets in Continuous Logic<br />
<br />
Abstract: In order to be useful the notion of a 'definable set' in continuous logic is stricter than a naive comparison to discrete logic<br />
would suggest. As a consequence, even in relatively tame theories there can be very few definable sets. For example, there is a<br />
superstable theory with no non-trivial definable sets. As we'll see, however, there are many definable sets in omega-stable,<br />
omega-categorical, and other small theories.<br />
<br />
=== February 19, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: Proper forcing<br />
<br />
Abstract: Although a given forcing notion may have nice properties on its own, those properties might vanish when we apply it repeatedly.<br />
Early preservation results (that is, theorems saying that the iteration of forcings with a nice property retains that nice property)<br />
were fairly limited, and things really got off the ground with Shelah's invention of "proper forcing." Roughly speaking, a forcing is<br />
proper if it can be approximated by elementary submodels of the universe in a particularly nice way. I'll define proper forcing and<br />
sketch some applications. <br />
<br />
=== February 26, Patrick Nicodemus ===<br />
<br />
Title: A survey of computable and constructive mathematics in economic history<br />
<br />
=== March 5, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===<br />
<br />
Title: Convexly Orderable Groups <br />
<br />
=== March 12, [https://math.nd.edu/people/visiting-faculty/daniel-turetsky/ Dan Turetsky] (University of Notre Dame) ===<br />
<br />
Title: Structural Jump<br />
<br />
=== March 19, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===<br />
<br />
Title: Networks and degrees of points in non-second countable spaces<br />
<br />
=== April 2, Wil Cocke ===<br />
<br />
Title: Characterizing Finite Nilpotent Groups via Word Maps<br />
<br />
Abstract: In this talk, we will examine a novel characterization of finite nilpotent groups using the probability distributions induced by word maps. In particular we show that a finite group is nilpotent if and only if every surjective word map has fibers of uniform size.<br />
<br />
=== April 9, Tejas Bhojraj ===<br />
<br />
Title: Quantum Randomness<br />
<br />
Abstract: I will read the paper by Nies and Scholz where they define a notion of algorithmic randomness for infinite sequences of quantum bits (qubits). This talk will cover the basic notions of quantum randomness on which my talk on Tuesday will be based. <br />
<br />
=== April 16, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===<br />
<br />
Title: What can we say about sets made by the union of Turing equivalence classes?<br />
<br />
Abstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type 'the rationals' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes?<br />
<br />
This topic hasn't been deeply studied. In this talk I will focus principally on famous order types and answer whether they can be achieved or not. Furthermore, I will explain some possible connections with the automorphism problem of the Turing degrees.<br />
<br />
This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation.(hopefully).<br />
<br />
=== April 23, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] (Thesis Defense) Start 3:45 Room B231===<br />
<br />
Title: Cototal enumeration degrees and their applications to effective mathematics <br />
<br />
Abstract: The enumeration degrees measure the relative computational difficulty of enumerating sets of natural numbers. Unlike the Turing degrees, the enumeration degrees of a set and its complement need not be comparable. A set is total if it is enumeration above its complement. Taken together, the enumeration degrees of total sets form an embedded copy of the Turing degrees within the enumeration degrees. A set of natural numbers is cototal if it is enumeration reducible to its complement. Surprisingly, the degrees of cototal sets, the cototal degrees, form an intermediate structure strictly between the total degrees and the enumeration degrees. <br />
<br />
Jeandel observed that cototal sets appear in a wide class of structures: as the word problems of simple groups, as the languages of minimal subshifts, and more generally as the maximal points of any c.e. quasivariety. In the case of minimal subshifts, the enumeration degree of the subshift's language determines the subshift's Turing degree spectrum: the collection of Turing degrees obtained by the points of the subshift. We prove that cototality precisely characterizes the Turing degree spectra of minimal subshifts: the degree spectra of nontrivial minimal subshifts are precisely the cototal enumeration cones. On the way to this result, we will give several other characterizations of the cototal degrees, including as the degrees of maximal anti-chain complements on <math>\omega^{<\omega}</math>, and as the degrees of enumeration-pointed trees on <math>2^{<\omega}</math>, and we will remark on some additional applications of these characterizations.<br />
<br />
=== April 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde]===<br />
<br />
Title: Definibility of the Frobenius orbits and an application to sets of rational distances.<br />
<br />
Abstract: In this talk I'll present a paper by Hector Pastén. We will talk about how having a formula that identify a Frobenius orbits can help you show an analogue case of Hilbert's tenth problem (the one asking for an algorithm that tells you if a diophantine equation is solvable or not).<br />
<br />
Finally, if time permits, we will do an application that solves the existence of a dense set in the plane with rational distances, assuming some form of the ABC conjecture. This last question was propose by Erdös and Ulam.<br />
<br />
== Fall 2017 ==<br />
<br />
=== September 11, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== September 18, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: The Kunen inconsistency<br />
<br />
Abstract: While early large cardinal axioms were usually defined combinatorially - e.g., cardinals satisfying a version of Ramsey's<br />
theorem - later focus shifted to model-theoretic definitions, specifically definitions in terms of elementary embeddings of the<br />
whole universe of sets. At the lowest level, a measurable cardinal is one which is the least cardinal moved (= critical point) by a<br />
nontrivial elementary embedding from V into some inner model M.<br />
<br />
There are several variations on this theme yielding stronger and stronger large cardinal notions; one of the most important is the<br />
inclusion of *correctness properties* of the target model M. The strongest such correctness property is total correctness: M=V. The<br />
critical point of an elementary embedding from V to V is called a *Reinhardt cardinal*. Shortly after their introduction in Reinhardt's<br />
thesis, however, the existence of a Reinhardt cardinal was shown to be inconsistent with ZFC.<br />
<br />
I'll present this argument, and talk a bit about the role of choice. <br />
<br />
=== September 25, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: Hindman's theorem via ultrafilters<br />
<br />
Abstract: Hindman's theorem is a Ramsey-type theorem in additive combinatorics: if we color the natural numbers with two colors, there is an infinite set such that any *finite sum* from that set has the same color as any other finite sum. There are (to my knowledge) two proofs of Hindman's theorem: one of them is a complicated mess of combinatorics, and the other consists of cheating wildly. We'll do.<br />
<br />
=== October 2, James Hanson ===<br />
<br />
Title: The Gromov-Hausdorff metric on type space in continuous logic<br />
<br />
Abstract: The Gromov-Hausdorff metric is a notion of the 'distance' between two metric spaces. Although it is typically studied in the context of compact or locally compact metric spaces, the definition is sensible even when applied to non-compact metric spaces, but in that context it is only a pseudo-metric: there are non-isomorphic metric spaces with Gromov-Hausdorff distance 0. This gives rise to an equivalence relation that is slightly coarser than isomorphism. There are continuous first-order theories which are categorical with regards to this equivalence relation while failing to be isometrically categorical, so it is natural to look for analogs of the Ryll-Nardzewski theorem and Morley's theorem, but before we can do any of that, it'll be necessary to learn about the "topometric" structure induced on type space by the Gromov-Hausdorff metric.<br />
<br />
=== October 9, James Hanson ===<br />
<br />
Title: Morley rank and stability in continuous logic<br />
<br />
Abstract: There are various ways of counting the 'size' of subsets of metric spaces. Using these we can do a kind of Cantor-Bendixson analysis on type spaces in continuous first-order theories, and thereby define a notion of Morley rank. More directly we can define<br />
> the 'correct' notion of stability in the continuous setting. There are also natural Gromov-Hausdorff (GH) analogs of these notions. With this we'll prove that inseparably categorical theories have atomic models over arbitrary sets, which is an important step in the proof of Morley's theorem in this setting. The same proof with essentially cosmetic changes gives that inseparably GH-categorical theories have 'GH-atomic' models over arbitrary sets, but GH-atomic models fail to be GH-unique in general.<br />
<br />
=== October 23, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===<br />
<br />
Title: Boxy sets in ordered convexly-orderable structures.<br />
<br />
=== October 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===<br />
<br />
Title: Dancing SCCA and other Coloring Axioms<br />
<br />
Abstract: In this talk I will talk about some axioms that are closely related to SOCA (Semi Open Coloring Axiom), being the main protagonist SCCA (Semi Clopen Coloring Axiom). I will give a motivation on the statements of both axioms, a little historic perspective and showing that both axioms coincide for separable Baire spaces. This is a work in progress, so I will share some open questions that I'm happy to discuss.<br />
<br />
=== November 6, Wil Cocke ===<br />
<br />
Title: Two new characterizations of nilpotent groups<br />
<br />
Abstract: We will give two new characterizations of finite nilpotent groups. One using information about the order of products of elements of prime order and the other using the induced probability distribution from word maps.<br />
<br />
Or...<br />
<br />
Title: Centralizing Propagating Properties of Groups<br />
<br />
Abstract: We will examine some sentences known to have finite spectrum when conjoined with the theory of groups. Hopefully we will be able to find new examples. <br />
<br />
=== November 13, [https://www.math.wisc.edu/~lempp/ Steffen Lempp] ===<br />
<br />
Title: The computational complexity of properties of finitely presented groups<br />
<br />
Abstract: I will survey index set complexity results on finitely presented groups.<br />
<br />
=== November 20, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===<br />
<br />
Title: Strong Difference Randomness<br />
<br />
Abstract: The difference randoms were introduced by Franklin and Ng to characterize the incomplete Martin-Löf randoms. More recently, Bienvenu and Porter introduced the strong difference randoms, obtained by imposing the Solovay condition over the class of difference tests. I will give a Demuth test characterization of the strong difference randoms, along with a lowness characterization of them among the Martin-Löf randoms. <br />
<br />
=== December 4, Tejas Bhojraj ===<br />
<br />
Title: Quantum Algorithmic Randomness<br />
<br />
Abstract: I will discuss the recent paper by Nies and Scholz where they define quantum Martin-Lof randomness (q-MLR) for infinite sequences of qubits. If time permits, I will introduce the notion of quantum Solovay randomness and show that it is equivalent to q-MLR in some special cases.<br />
<br />
=== December 11, Grigory Terlov ===<br />
<br />
Title: The Logic of Erdős–Rényi Graphs</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Logic_Graduate_Seminar,_previous_semesters&diff=16023Logic Graduate Seminar, previous semesters2018-09-20T18:10:09Z<p>Ongay: Created page with "This is an historic listing of the talks in the Logic Student Seminar. == Spring 2018 == === January 29, Organizational meeting === This day we decided the schedule for the..."</p>
<hr />
<div>This is an historic listing of the talks in the Logic Student Seminar.<br />
<br />
== Spring 2018 ==<br />
<br />
=== January 29, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== February 5, [http://www.math.wisc.edu/~andrews/ Uri Andrews] ===<br />
<br />
Title: Building Models of Strongly Minimal Theories - Part 1<br />
<br />
Abstract: Since I'm talking in the Tuesday seminar as well, I'll use the Monday seminar talk to do some background on the topic and some<br />
lemmas that will go into the proofs in Tuesday's talk. There will be (I hope) some theorems of interest to see on both days, and both on<br />
the general topic of answering the following question: What do you need to know about a strongly minimal theory in order to compute<br />
copies of all of its countable models. I'll start with a definition for strongly minimal theories and build up from there.<br />
<br />
=== February 12, James Hanson ===<br />
<br />
Title: Finding Definable Sets in Continuous Logic<br />
<br />
Abstract: In order to be useful the notion of a 'definable set' in continuous logic is stricter than a naive comparison to discrete logic<br />
would suggest. As a consequence, even in relatively tame theories there can be very few definable sets. For example, there is a<br />
superstable theory with no non-trivial definable sets. As we'll see, however, there are many definable sets in omega-stable,<br />
omega-categorical, and other small theories.<br />
<br />
=== February 19, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: Proper forcing<br />
<br />
Abstract: Although a given forcing notion may have nice properties on its own, those properties might vanish when we apply it repeatedly.<br />
Early preservation results (that is, theorems saying that the iteration of forcings with a nice property retains that nice property)<br />
were fairly limited, and things really got off the ground with Shelah's invention of "proper forcing." Roughly speaking, a forcing is<br />
proper if it can be approximated by elementary submodels of the universe in a particularly nice way. I'll define proper forcing and<br />
sketch some applications. <br />
<br />
=== February 26, Patrick Nicodemus ===<br />
<br />
Title: A survey of computable and constructive mathematics in economic history<br />
<br />
=== March 5, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===<br />
<br />
Title: Convexly Orderable Groups <br />
<br />
=== March 12, [https://math.nd.edu/people/visiting-faculty/daniel-turetsky/ Dan Turetsky] (University of Notre Dame) ===<br />
<br />
Title: Structural Jump<br />
<br />
=== March 19, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===<br />
<br />
Title: Networks and degrees of points in non-second countable spaces<br />
<br />
=== April 2, Wil Cocke ===<br />
<br />
Title: Characterizing Finite Nilpotent Groups via Word Maps<br />
<br />
Abstract: In this talk, we will examine a novel characterization of finite nilpotent groups using the probability distributions induced by word maps. In particular we show that a finite group is nilpotent if and only if every surjective word map has fibers of uniform size.<br />
<br />
=== April 9, Tejas Bhojraj ===<br />
<br />
Title: Quantum Randomness<br />
<br />
Abstract: I will read the paper by Nies and Scholz where they define a notion of algorithmic randomness for infinite sequences of quantum bits (qubits). This talk will cover the basic notions of quantum randomness on which my talk on Tuesday will be based. <br />
<br />
=== April 16, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===<br />
<br />
Title: What can we say about sets made by the union of Turing equivalence classes?<br />
<br />
Abstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type 'the rationals' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes?<br />
<br />
This topic hasn't been deeply studied. In this talk I will focus principally on famous order types and answer whether they can be achieved or not. Furthermore, I will explain some possible connections with the automorphism problem of the Turing degrees.<br />
<br />
This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation.(hopefully).<br />
<br />
=== April 23, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] (Thesis Defense) Start 3:45 Room B231===<br />
<br />
Title: Cototal enumeration degrees and their applications to effective mathematics <br />
<br />
Abstract: The enumeration degrees measure the relative computational difficulty of enumerating sets of natural numbers. Unlike the Turing degrees, the enumeration degrees of a set and its complement need not be comparable. A set is total if it is enumeration above its complement. Taken together, the enumeration degrees of total sets form an embedded copy of the Turing degrees within the enumeration degrees. A set of natural numbers is cototal if it is enumeration reducible to its complement. Surprisingly, the degrees of cototal sets, the cototal degrees, form an intermediate structure strictly between the total degrees and the enumeration degrees. <br />
<br />
Jeandel observed that cototal sets appear in a wide class of structures: as the word problems of simple groups, as the languages of minimal subshifts, and more generally as the maximal points of any c.e. quasivariety. In the case of minimal subshifts, the enumeration degree of the subshift's language determines the subshift's Turing degree spectrum: the collection of Turing degrees obtained by the points of the subshift. We prove that cototality precisely characterizes the Turing degree spectra of minimal subshifts: the degree spectra of nontrivial minimal subshifts are precisely the cototal enumeration cones. On the way to this result, we will give several other characterizations of the cototal degrees, including as the degrees of maximal anti-chain complements on <math>\omega^{<\omega}</math>, and as the degrees of enumeration-pointed trees on <math>2^{<\omega}</math>, and we will remark on some additional applications of these characterizations.<br />
<br />
=== April 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde]===<br />
<br />
Title: Definibility of the Frobenius orbits and an application to sets of rational distances.<br />
<br />
Abstract: In this talk I'll present a paper by Hector Pastén. We will talk about how having a formula that identify a Frobenius orbits can help you show an analogue case of Hilbert's tenth problem (the one asking for an algorithm that tells you if a diophantine equation is solvable or not).<br />
<br />
Finally, if time permits, we will do an application that solves the existence of a dense set in the plane with rational distances, assuming some form of the ABC conjecture. This last question was propose by Erdös and Ulam.<br />
<br />
== Fall 2017 ==<br />
<br />
=== September 11, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== September 18, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: The Kunen inconsistency<br />
<br />
Abstract: While early large cardinal axioms were usually defined combinatorially - e.g., cardinals satisfying a version of Ramsey's<br />
theorem - later focus shifted to model-theoretic definitions, specifically definitions in terms of elementary embeddings of the<br />
whole universe of sets. At the lowest level, a measurable cardinal is one which is the least cardinal moved (= critical point) by a<br />
nontrivial elementary embedding from V into some inner model M.<br />
<br />
There are several variations on this theme yielding stronger and stronger large cardinal notions; one of the most important is the<br />
inclusion of *correctness properties* of the target model M. The strongest such correctness property is total correctness: M=V. The<br />
critical point of an elementary embedding from V to V is called a *Reinhardt cardinal*. Shortly after their introduction in Reinhardt's<br />
thesis, however, the existence of a Reinhardt cardinal was shown to be inconsistent with ZFC.<br />
<br />
I'll present this argument, and talk a bit about the role of choice. <br />
<br />
=== September 25, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: Hindman's theorem via ultrafilters<br />
<br />
Abstract: Hindman's theorem is a Ramsey-type theorem in additive combinatorics: if we color the natural numbers with two colors, there is an infinite set such that any *finite sum* from that set has the same color as any other finite sum. There are (to my knowledge) two proofs of Hindman's theorem: one of them is a complicated mess of combinatorics, and the other consists of cheating wildly. We'll do.<br />
<br />
=== October 2, James Hanson ===<br />
<br />
Title: The Gromov-Hausdorff metric on type space in continuous logic<br />
<br />
Abstract: The Gromov-Hausdorff metric is a notion of the 'distance' between two metric spaces. Although it is typically studied in the context of compact or locally compact metric spaces, the definition is sensible even when applied to non-compact metric spaces, but in that context it is only a pseudo-metric: there are non-isomorphic metric spaces with Gromov-Hausdorff distance 0. This gives rise to an equivalence relation that is slightly coarser than isomorphism. There are continuous first-order theories which are categorical with regards to this equivalence relation while failing to be isometrically categorical, so it is natural to look for analogs of the Ryll-Nardzewski theorem and Morley's theorem, but before we can do any of that, it'll be necessary to learn about the "topometric" structure induced on type space by the Gromov-Hausdorff metric.<br />
<br />
=== October 9, James Hanson ===<br />
<br />
Title: Morley rank and stability in continuous logic<br />
<br />
Abstract: There are various ways of counting the 'size' of subsets of metric spaces. Using these we can do a kind of Cantor-Bendixson analysis on type spaces in continuous first-order theories, and thereby define a notion of Morley rank. More directly we can define<br />
> the 'correct' notion of stability in the continuous setting. There are also natural Gromov-Hausdorff (GH) analogs of these notions. With this we'll prove that inseparably categorical theories have atomic models over arbitrary sets, which is an important step in the proof of Morley's theorem in this setting. The same proof with essentially cosmetic changes gives that inseparably GH-categorical theories have 'GH-atomic' models over arbitrary sets, but GH-atomic models fail to be GH-unique in general.<br />
<br />
=== October 23, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===<br />
<br />
Title: Boxy sets in ordered convexly-orderable structures.<br />
<br />
=== October 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===<br />
<br />
Title: Dancing SCCA and other Coloring Axioms<br />
<br />
Abstract: In this talk I will talk about some axioms that are closely related to SOCA (Semi Open Coloring Axiom), being the main protagonist SCCA (Semi Clopen Coloring Axiom). I will give a motivation on the statements of both axioms, a little historic perspective and showing that both axioms coincide for separable Baire spaces. This is a work in progress, so I will share some open questions that I'm happy to discuss.<br />
<br />
=== November 6, Wil Cocke ===<br />
<br />
Title: Two new characterizations of nilpotent groups<br />
<br />
Abstract: We will give two new characterizations of finite nilpotent groups. One using information about the order of products of elements of prime order and the other using the induced probability distribution from word maps.<br />
<br />
Or...<br />
<br />
Title: Centralizing Propagating Properties of Groups<br />
<br />
Abstract: We will examine some sentences known to have finite spectrum when conjoined with the theory of groups. Hopefully we will be able to find new examples. <br />
<br />
=== November 13, [https://www.math.wisc.edu/~lempp/ Steffen Lempp] ===<br />
<br />
Title: The computational complexity of properties of finitely presented groups<br />
<br />
Abstract: I will survey index set complexity results on finitely presented groups.<br />
<br />
=== November 20, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===<br />
<br />
Title: Strong Difference Randomness<br />
<br />
Abstract: The difference randoms were introduced by Franklin and Ng to characterize the incomplete Martin-Löf randoms. More recently, Bienvenu and Porter introduced the strong difference randoms, obtained by imposing the Solovay condition over the class of difference tests. I will give a Demuth test characterization of the strong difference randoms, along with a lowness characterization of them among the Martin-Löf randoms. <br />
<br />
=== December 4, Tejas Bhojraj ===<br />
<br />
Title: Quantum Algorithmic Randomness<br />
<br />
Abstract: I will discuss the recent paper by Nies and Scholz where they define quantum Martin-Lof randomness (q-MLR) for infinite sequences of qubits. If time permits, I will introduce the notion of quantum Solovay randomness and show that it is equivalent to q-MLR in some special cases.<br />
<br />
=== December 11, Grigory Terlov ===<br />
<br />
Title: The Logic of Erdős–Rényi Graphs</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Logic_Seminar&diff=15434Graduate Logic Seminar2018-04-19T00:34:40Z<p>Ongay: </p>
<hr />
<div>The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.<br />
<br />
* '''When:''' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).<br />
* '''Where:''' Van Vleck B235 (unless otherwise announced).<br />
* '''Organizers:''' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava]<br />
<br />
Talks schedule are arrange and decide at the beginning of each semester. If you would like to participate, please contact one of the organizers.<br />
<br />
== Spring 2018 ==<br />
<br />
=== January 29, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== February 5, [http://www.math.wisc.edu/~andrews/ Uri Andrews] ===<br />
<br />
Title: Building Models of Strongly Minimal Theories - Part 1<br />
<br />
Abstract: Since I'm talking in the Tuesday seminar as well, I'll use the Monday seminar talk to do some background on the topic and some<br />
lemmas that will go into the proofs in Tuesday's talk. There will be (I hope) some theorems of interest to see on both days, and both on<br />
the general topic of answering the following question: What do you need to know about a strongly minimal theory in order to compute<br />
copies of all of its countable models. I'll start with a definition for strongly minimal theories and build up from there.<br />
<br />
=== February 12, James Hanson ===<br />
<br />
Title: Finding Definable Sets in Continuous Logic<br />
<br />
Abstract: In order to be useful the notion of a 'definable set' in continuous logic is stricter than a naive comparison to discrete logic<br />
would suggest. As a consequence, even in relatively tame theories there can be very few definable sets. For example, there is a<br />
superstable theory with no non-trivial definable sets. As we'll see, however, there are many definable sets in omega-stable,<br />
omega-categorical, and other small theories.<br />
<br />
=== February 19, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: Proper forcing<br />
<br />
Abstract: Although a given forcing notion may have nice properties on its own, those properties might vanish when we apply it repeatedly.<br />
Early preservation results (that is, theorems saying that the iteration of forcings with a nice property retains that nice property)<br />
were fairly limited, and things really got off the ground with Shelah's invention of "proper forcing." Roughly speaking, a forcing is<br />
proper if it can be approximated by elementary submodels of the universe in a particularly nice way. I'll define proper forcing and<br />
sketch some applications. <br />
<br />
=== February 26, Patrick Nicodemus ===<br />
<br />
Title: A survey of computable and constructive mathematics in economic history<br />
<br />
=== March 5, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===<br />
<br />
Title: Convexly Orderable Groups <br />
<br />
=== March 12, [https://math.nd.edu/people/visiting-faculty/daniel-turetsky/ Dan Turetsky] (University of Notre Dame) ===<br />
<br />
Title: Structural Jump<br />
<br />
=== March 19, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===<br />
<br />
Title: Networks and degrees of points in non-second countable spaces<br />
<br />
=== April 2, Wil Cocke ===<br />
<br />
Title: Characterizing Finite Nilpotent Groups via Word Maps<br />
<br />
Abstract: In this talk, we will examine a novel characterization of finite nilpotent groups using the probability distributions induced by word maps. In particular we show that a finite group is nilpotent if and only if every surjective word map has fibers of uniform size.<br />
<br />
=== April 9, Tejas Bhojraj ===<br />
<br />
Title: Quantum Randomness<br />
<br />
Abstract: I will read the paper by Nies and Scholz where they define a notion of algorithmic randomness for infinite sequences of quantum bits (qubits). This talk will cover the basic notions of quantum randomness on which my talk on Tuesday will be based. <br />
<br />
=== April 16, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===<br />
<br />
Title: What can we say about sets made by the union of Turing equivalence classes?<br />
<br />
Abstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type 'the rationals' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes?<br />
<br />
This topic hasn't been deeply studied. In this talk I will focus principally on famous order types and answer whether they can be achieved or not. Furthermore, I will explain some possible connections with the automorphism problem of the Turing degrees.<br />
<br />
This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation.(hopefully).<br />
<br />
=== April 23, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] (Thesis Defense) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== April 30, [http://www.math.uconn.edu/~westrick/ Linda Brown Westrick] (from University Of Connecticut) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
== Fall 2017 ==<br />
<br />
=== September 11, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== September 18, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: The Kunen inconsistency<br />
<br />
Abstract: While early large cardinal axioms were usually defined combinatorially - e.g., cardinals satisfying a version of Ramsey's<br />
theorem - later focus shifted to model-theoretic definitions, specifically definitions in terms of elementary embeddings of the<br />
whole universe of sets. At the lowest level, a measurable cardinal is one which is the least cardinal moved (= critical point) by a<br />
nontrivial elementary embedding from V into some inner model M.<br />
<br />
There are several variations on this theme yielding stronger and stronger large cardinal notions; one of the most important is the<br />
inclusion of *correctness properties* of the target model M. The strongest such correctness property is total correctness: M=V. The<br />
critical point of an elementary embedding from V to V is called a *Reinhardt cardinal*. Shortly after their introduction in Reinhardt's<br />
thesis, however, the existence of a Reinhardt cardinal was shown to be inconsistent with ZFC.<br />
<br />
I'll present this argument, and talk a bit about the role of choice. <br />
<br />
=== September 25, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===<br />
<br />
Title: Hindman's theorem via ultrafilters<br />
<br />
Abstract: Hindman's theorem is a Ramsey-type theorem in additive combinatorics: if we color the natural numbers with two colors, there is an infinite set such that any *finite sum* from that set has the same color as any other finite sum. There are (to my knowledge) two proofs of Hindman's theorem: one of them is a complicated mess of combinatorics, and the other consists of cheating wildly. We'll do.<br />
<br />
=== October 2, James Hanson ===<br />
<br />
Title: The Gromov-Hausdorff metric on type space in continuous logic<br />
<br />
Abstract: The Gromov-Hausdorff metric is a notion of the 'distance' between two metric spaces. Although it is typically studied in the context of compact or locally compact metric spaces, the definition is sensible even when applied to non-compact metric spaces, but in that context it is only a pseudo-metric: there are non-isomorphic metric spaces with Gromov-Hausdorff distance 0. This gives rise to an equivalence relation that is slightly coarser than isomorphism. There are continuous first-order theories which are categorical with regards to this equivalence relation while failing to be isometrically categorical, so it is natural to look for analogs of the Ryll-Nardzewski theorem and Morley's theorem, but before we can do any of that, it'll be necessary to learn about the "topometric" structure induced on type space by the Gromov-Hausdorff metric.<br />
<br />
=== October 9, James Hanson ===<br />
<br />
Title: Morley rank and stability in continuous logic<br />
<br />
Abstract: There are various ways of counting the 'size' of subsets of metric spaces. Using these we can do a kind of Cantor-Bendixson analysis on type spaces in continuous first-order theories, and thereby define a notion of Morley rank. More directly we can define<br />
> the 'correct' notion of stability in the continuous setting. There are also natural Gromov-Hausdorff (GH) analogs of these notions. With this we'll prove that inseparably categorical theories have atomic models over arbitrary sets, which is an important step in the proof of Morley's theorem in this setting. The same proof with essentially cosmetic changes gives that inseparably GH-categorical theories have 'GH-atomic' models over arbitrary sets, but GH-atomic models fail to be GH-unique in general.<br />
<br />
=== October 23, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===<br />
<br />
Title: Boxy sets in ordered convexly-orderable structures.<br />
<br />
=== October 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===<br />
<br />
Title: Dancing SCCA and other Coloring Axioms<br />
<br />
Abstract: In this talk I will talk about some axioms that are closely related to SOCA (Semi Open Coloring Axiom), being the main protagonist SCCA (Semi Clopen Coloring Axiom). I will give a motivation on the statements of both axioms, a little historic perspective and showing that both axioms coincide for separable Baire spaces. This is a work in progress, so I will share some open questions that I'm happy to discuss.<br />
<br />
=== November 6, Wil Cocke ===<br />
<br />
Title: Two new characterizations of nilpotent groups<br />
<br />
Abstract: We will give two new characterizations of finite nilpotent groups. One using information about the order of products of elements of prime order and the other using the induced probability distribution from word maps.<br />
<br />
Or...<br />
<br />
Title: Centralizing Propagating Properties of Groups<br />
<br />
Abstract: We will examine some sentences known to have finite spectrum when conjoined with the theory of groups. Hopefully we will be able to find new examples. <br />
<br />
=== November 13, [https://www.math.wisc.edu/~lempp/ Steffen Lempp] ===<br />
<br />
Title: The computational complexity of properties of finitely presented groups<br />
<br />
Abstract: I will survey index set complexity results on finitely presented groups.<br />
<br />
=== November 20, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===<br />
<br />
Title: Strong Difference Randomness<br />
<br />
Abstract: The difference randoms were introduced by Franklin and Ng to characterize the incomplete Martin-Löf randoms. More recently, Bienvenu and Porter introduced the strong difference randoms, obtained by imposing the Solovay condition over the class of difference tests. I will give a Demuth test characterization of the strong difference randoms, along with a lowness characterization of them among the Martin-Löf randoms. <br />
<br />
=== December 4, Tejas Bhojraj ===<br />
<br />
Title: Quantum Algorithmic Randomness<br />
<br />
Abstract: I will discuss the recent paper by Nies and Scholz where they define quantum Martin-Lof randomness (q-MLR) for infinite sequences of qubits. If time permits, I will introduce the notion of quantum Solovay randomness and show that it is equivalent to q-MLR in some special cases.<br />
<br />
=== December 11, Grigory Terlov ===<br />
<br />
Title: The Logic of Erdős–Rényi Graphs<br />
<br />
==Previous Years==<br />
<br />
The schedule of talks from past semesters can be found [[Logic Graduate Seminar, previous semesters|here]].</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Logic_Seminar&diff=15432Graduate Logic Seminar2018-04-19T00:01:38Z<p>Ongay: </p>
<hr />
<div>The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.<br />
<br />
* '''When:''' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).<br />
* '''Where:''' Van Vleck B235 (unless otherwise announced).<br />
* '''Organizers:''' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava]<br />
<br />
Talks schedule are arrange and decide at the beginning of each semester. If you would like to participate, please contact one of the organizers.<br />
<br />
== Spring 2018 ==<br />
<br />
=== January 29, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== February 5, Uri Andrews ===<br />
<br />
Title: Building Models of Strongly Minimal Theories - Part 1<br />
<br />
Abstract: Since I'm talking in the Tuesday seminar as well, I'll use<br />
the Monday seminar talk to do some background on the topic and some<br />
lemmas that will go into the proofs in Tuesday's talk. There will be<br />
(I hope) some theorems of interest to see on both days, and both on<br />
the general topic of answering the following question: What do you<br />
need to know about a strongly minimal theory in order to compute<br />
copies of all of its countable models. I'll start with a definition<br />
for strongly minimal theories and build up from there.<br />
<br />
=== February 12, James Hanson ===<br />
<br />
Title: Finding Definable Sets in Continuous Logic<br />
<br />
Abstract: In order to be useful the notion of a 'definable set' in<br />
continuous logic is stricter than a naive comparison to discrete logic<br />
would suggest. As a consequence, even in relatively tame theories<br />
there can be very few definable sets. For example, there is a<br />
superstable theory with no non-trivial definable sets. As we'll see,<br />
however, there are many definable sets in omega-stable,<br />
omega-categorical, and other small theories.<br />
<br />
=== February 19, Noah Schweber ===<br />
<br />
Title: Proper forcing<br />
<br />
Abstract: Although a given forcing notion may have nice properties on<br />
its own, those properties might vanish when we apply it repeatedly.<br />
Early preservation results (that is, theorems saying that the<br />
iteration of forcings with a nice property retains that nice property)<br />
were fairly limited, and things really got off the ground with<br />
Shelah's invention of "proper forcing." Roughly speaking, a forcing is<br />
proper if it can be approximated by elementary submodels of the<br />
universe in a particularly nice way. I'll define proper forcing and<br />
sketch some applications. <br />
<br />
=== February 26, Patrick Nicodemus ===<br />
<br />
Title: A survey of computable and constructive mathematics in economic history<br />
<br />
=== March 5, Tamvana Makulumi ===<br />
<br />
Title: Convexly Orderable Groups <br />
<br />
=== March 12, Dan Turetsky (University of Notre Dame) ===<br />
<br />
Title: Structural Jump<br />
<br />
=== March 19, Ethan McCarthy ===<br />
<br />
Title: Networks and degrees of points in non-second countable spaces<br />
<br />
=== April 2, Wil Cocke ===<br />
<br />
Title: Characterizing Finite Nilpotent Groups via Word Maps<br />
<br />
Abstract: In this talk, we will examine a novel characterization of finite<br />
nilpotent groups using the probability distributions induced by word<br />
maps. In particular we show that a finite group is nilpotent if and<br />
only if every surjective word map has fibers of uniform size.<br />
<br />
=== April 9, Tejas Bhojraj ===<br />
<br />
Title: Quantum Randomness<br />
<br />
Abstract: I will read the paper by Nies and Scholz where they define a notion of<br />
algorithmic randomness for infinite sequences of quantum bits<br />
(qubits). This talk will cover the basic notions of quantum randomness<br />
on which my talk on Tuesday will be based. <br />
<br />
=== April 16, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===<br />
<br />
Title: What can we say about sets made by the union of Turing equivalence classes?<br />
<br />
Abstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type 'the rationals' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes?<br />
<br />
This topic hasn't been deeply studied. In this talk I will focus principally on famous order types and answer whether they can be achieved or not. Furthermore, I will explain some possible connections with the automorphism problem of the Turing degrees.<br />
<br />
This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation (hopefully).<br />
<br />
=== April 23, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] (Thesis Defense) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== April 30, [http://www.math.uconn.edu/~westrick/ Linda Brown Westrick] (from University Of Connecticut) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== May 7, TBA ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
== Fall 2017 ==<br />
<br />
=== September 11, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== September 18, (person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== September 25, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 2, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 9, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 16, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 23, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 30, Iván Ongay-Valverde ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 6, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 13, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 20, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 27, (Person) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== December 4, (Person) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== December 11, (Person) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
==Previous Years==<br />
<br />
The schedule of talks from past semesters can be found [[Logic Graduate Seminar, previous semesters|here]].</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Logic_Seminar&diff=15427Graduate Logic Seminar2018-04-16T19:44:47Z<p>Ongay: </p>
<hr />
<div>The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.<br />
<br />
* '''When:''' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).<br />
* '''Where:''' Van Vleck B235 (unless otherwise announced).<br />
* '''Organizers:''' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava]<br />
<br />
Talks schedule are arrange and decide at the beginning of each semester. If you would like to participate, please contact one of the organizers.<br />
<br />
== Spring 2018 ==<br />
<br />
=== January 29, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== February 5, (person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== February 12, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== February 19, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== February 26, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== March 5, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== March 12, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== March 19, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== April 2, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== April 9, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== April 16, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===<br />
<br />
Title: What can we say about sets made by the union of Turing equivalence classes?<br />
<br />
Abstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type 'the rationals' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes?<br />
<br />
This topic hasn't been deeply studied. In this talk I will focus principally on famous order types and answer whether they can be achieved or not. Furthermore, I will explain some possible connections with the automorphism problem of the Turing degrees.<br />
<br />
This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation (hopefully).<br />
<br />
=== April 23, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] (Thesis Defense) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== April 30, [http://www.math.uconn.edu/~westrick/ Linda Brown Westrick] (from University Of Connecticut) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== May 7, TBA ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
== Fall 2017 ==<br />
<br />
=== September 11, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== September 18, (person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== September 25, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 2, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 9, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 16, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 23, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 30, Iván Ongay-Valverde ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 6, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 13, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 20, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 27, (Person) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== December 4, (Person) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== December 11, (Person) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
==Previous Years==<br />
<br />
The schedule of talks from past semesters can be found [[Logic Graduate Seminar, previous semesters|here]].</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Main_Page&diff=15426Main Page2018-04-16T19:36:35Z<p>Ongay: /* Graduate Student Seminars */</p>
<hr />
<div><br />
== Welcome to the University of Wisconsin Math Department Wiki ==<br />
<br />
This site is by and for the faculty, students and staff of the UW Mathematics Department. It contains useful information about the department, not always available from other sources. Pages can only be edited by members of the department but are viewable by everyone. <br />
<br />
*[[Getting Around Van Vleck]]<br />
<br />
*[[Computer Help]] <br />
<br />
*[[Connecting/Using our research servers]]<br />
<br />
*[[Graduate Student Guide]]<br />
<br />
*[[Teaching Resources]]<br />
<br />
== Research groups at UW-Madison ==<br />
<br />
*[[Algebra]]<br />
*[[Analysis]]<br />
*[[Applied|Applied Mathematics]]<br />
*[https://www.math.wisc.edu/wiki/index.php/Research_at_UW-Madison_in_DifferentialEquations Differential Equations]<br />
*[[Dynamics Special Lecture]]<br />
*[[Geometry and Topology]]<br />
* [http://www.math.wisc.edu/~lempp/logic.html Logic]<br />
*[[Probability]]<br />
<br />
== Math Seminars at UW-Madison ==<br />
<br />
*[[Colloquia|Colloquium]]<br />
*[[Algebra_and_Algebraic_Geometry_Seminar|Algebra and Algebraic Geometry Seminar]]<br />
*[[Analysis_Seminar|Analysis Seminar]]<br />
*[[Applied/ACMS|Applied and Computational Math Seminar]]<br />
*[http://www.math.wisc.edu/~zcharles/aas/index.html Applied Algebra Seminar]<br />
*[[Cookie_seminar|Cookie Seminar]]<br />
*[[Geometry_and_Topology_Seminar|Geometry and Topology Seminar]]<br />
*[[Group_Theory_Seminar|Group Theory Seminar]]<br />
*[[Networks_Seminar|Networks Seminar]]<br />
*[[NTS|Number Theory Seminar]]<br />
*[[PDE_Geometric_Analysis_seminar| PDE and Geometric Analysis Seminar]]<br />
*[[Probability_Seminar|Probability Seminar]]<br />
* [http://www.math.wisc.edu/~lempp/conf/swlc.html Southern Wisconsin Logic Colloquium]<br />
*[[Research Recruitment Seminar]]<br />
<br />
=== Graduate Student Seminars ===<br />
<br />
*[[AMS_Student_Chapter_Seminar|AMS Student Chapter Seminar]]<br />
*[[Graduate_Algebraic_Geometry_Seminar|Graduate Algebraic Geometry Seminar]]<br />
*[[Graduate_Applied_Algebra_Seminar|Graduate Applied Algebra Seminar]]<br />
*[[Applied/GPS| GPS Applied Math Seminar]]<br />
*[[NTSGrad_Spring_2018|Graduate Number Theory/Representation Theory Seminar]]<br />
*[[Symplectic_Geometry_Seminar|Symplectic Geometry Seminar]]<br />
*[[Math843Seminar| Math 843 Homework Seminar]]<br />
*[[Graduate_student_reading_seminar|Graduate Probability Reading Seminar]]<br />
*[[Summer_stacks|Summer 2012 Stacks Reading Group]]<br />
*[[Graduate_Student_Singularity_Theory]]<br />
*[[Graduate/Postdoc Topology and Singularities Seminar]]<br />
*[[Shimura Varieties Reading Group]]<br />
*[[Summer graduate harmonic analysis seminar]]<br />
*[[Graduate Logic Seminar]]<br />
<br />
=== Other ===<br />
*[[Madison Math Circle]]<br />
*[[High School Math Night]]<br />
*[http://www.siam-uw.org/ UW-Madison SIAM Student Chapter]<br />
*[http://www.math.wisc.edu/%7Emathclub/ UW-Madison Math Club]<br />
*[[Putnam Club]]<br />
*[[Undergraduate Math Competition]]<br />
*[[Basic Linux Seminar]]<br />
*[[Basic HTML Seminar]]<br />
<br />
== Graduate Program ==<br />
<br />
* [[Algebra Qualifying Exam]]<br />
* [[Analysis Qualifying Exam]]<br />
* [[Topology Qualifying Exam]]<br />
<br />
== Undergraduate Program ==<br />
<br />
* [[Overview of the undergraduate math program|Overview]]<br />
* [[Groups looking to hire students as tutors]]<br />
<br />
== Getting started with Wiki-stuff ==<br />
<br />
Consult the [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.<br />
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Logic_Seminar&diff=15424Graduate Logic Seminar2018-04-16T15:55:07Z<p>Ongay: The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning ma</p>
<hr />
<div>The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.<br />
<br />
* '''When:''' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).<br />
* '''Where:''' Van Vleck B235 (unless otherwise announced).<br />
* '''Organizers:''' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava]<br />
<br />
Talks schedule are arrange and decide at the beginning of each semester. If you would like to participate, please contact one of the organizers.<br />
<br />
== Spring 2018 ==<br />
<br />
=== January 29, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== February 5, (person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== February 12, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== February 19, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== February 26, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== March 5, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== March 12, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== March 19, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== April 2, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== April 9, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== April 16, Iván Ongay-Valverde ===<br />
<br />
Title: What can we say about sets made by the union of Turing equivalence classes?<br />
<br />
Abstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type 'the rationals' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes?<br />
<br />
This topic hasn't been deeply studied. In this talk I will focus principally on famous order types and answer whether they can be achieved or not. Furthermore, I will explain some possible connections with the automorphism problem of the Turing degrees.<br />
<br />
This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation (hopefully).<br />
<br />
=== April 23, Ethan (Defense) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== April 30, Linda ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== May 7, TBA ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
== Fall 2017 ==<br />
<br />
=== September 11, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== September 18, (person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== September 25, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 2, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 9, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 16, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 23, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 30, Iván Ongay-Valverde ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 6, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 13, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 20, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 27, (Person) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== December 4, (Person) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== December 11, (Person) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
==Previous Years==<br />
<br />
The schedule of talks from past semesters can be found [[Logic Graduate Seminar, previous semesters|here]].</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Logic_Seminar&diff=15423Graduate Logic Seminar2018-04-16T15:52:48Z<p>Ongay: The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning ma</p>
<hr />
<div>The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.<br />
<br />
* '''When:''' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).<br />
* '''Where:''' Van Vleck B235 (unless otherwise announced).<br />
* '''Organizers:''' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava]<br />
<br />
Talks schedule are arrange and decide at the beginning of each semester. If you would like to participate, please contact one of the organizers.<br />
<br />
%The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Spring 2018 ==<br />
<br />
=== January 29, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== February 5, (person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== February 12, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== February 19, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== February 26, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== March 5, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== March 12, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== March 19, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== April 2, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== April 9, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== April 16, Iván Ongay-Valverde ===<br />
<br />
Title: What can we say about sets made by the union of Turing equivalence classes?<br />
<br />
Abstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type 'the rationals' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes?<br />
<br />
This topic hasn't been deeply studied. In this talk I will focus principally on famous order types and answer whether they can be achieved or not. Furthermore, I will explain some possible connections with the automorphism problem of the Turing degrees.<br />
<br />
This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation (hopefully).<br />
<br />
=== April 23, Ethan (Defense) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== April 30, Linda ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== May 7, TBA ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
== Fall 2017 ==<br />
<br />
=== September 11, Organizational meeting ===<br />
<br />
This day we decided the schedule for the semester.<br />
<br />
=== September 18, (person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== September 25, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 2, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 9, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 16, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 23, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== October 30, Iván Ongay-Valverde ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 6, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 13, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 20, (Person) ===<br />
<br />
Title: <br />
<br />
Abstract: <br />
<br />
=== November 27, (Person) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== December 4, (Person) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
=== December 11, (Person) ===<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=AMS_Student_Chapter_Seminar&diff=13672AMS Student Chapter Seminar2017-04-17T17:46:46Z<p>Ongay: /* May 3, Iván Ongay-Valverde */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:00 PM – 3:30 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~hast/ Daniel Hast], [https://www.math.wisc.edu/~mrjulian/ Ryan Julian], Cullen McDonald, [https://www.math.wisc.edu/~zcharles/ Zachary Charles]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Spring 2017 ==<br />
<br />
=== January 25, Brandon Alberts ===<br />
<br />
Title: Ultraproducts - they aren't just for logicians<br />
<br />
Abstract: If any of you have attended a logic talk (or one of Ivan's donut seminar talks) you may have learned about ultraproducts as a weird way to mash sets together to get bigger sets in a nice way. Something particularly useful to set theorists, but maybe not so obviously useful to the rest of us. I will give an accessible introduction to ultraproducts and motivate their use in other areas of mathematics.<br />
<br />
=== February 1, Megan Maguire ===<br />
<br />
Title: Hyperbolic crochet workshop<br />
<br />
Abstract: TBA<br />
<br />
=== February 8, Cullen McDonald ===<br />
<br />
=== February 15, Paul Tveite ===<br />
<br />
Title: Fun with Hamel Bases!<br />
<br />
Abstract: If we view the real numbers as a vector field over the rationals, then of course they have a basis (assuming the AOC). This is called a Hamel basis and allows us to do some cool things. Among other things, we will define two periodic functions that sum to the identity function.<br />
<br />
=== February 22, Wil Cocke ===<br />
<br />
Title: Practical Graph Isomorphism<br />
<br />
Abstract: Some graphs are different and some graphs are the same. Sometimes graphs differ only in name. When you give me a graph, you've picked an order. But, is it the same graph across every border?<br />
<br />
=== March 1, Megan Maguire ===<br />
<br />
Title: I stole this talk from Jordan.<br />
<br />
Abstract: Stability is cool! And sometimes things we think don't have stability secretly do. This is an abridged version of a very cool talk I've seen Jordan give a couple times. All credit goes to him. Man, I should have stolen his abstract too.<br />
<br />
=== March 7, Liban Mohamed ===<br />
<br />
Title: Strichartz Estimates from Qualitative to Quantitative<br />
<br />
Abstract: Strichartz estimates are inequalities that give one way understand the decay of solutions to dispersive PDEs. This talk is an attempt to reconcile the formal statements with physical intuition.<br />
<br />
=== March 15, Zachary Charles ===<br />
<br />
Title: Netflix Problem and Chill<br />
<br />
Abstract: How are machine learning, matrix analysis, and Napoleon Dynamite related? Come find out!<br />
<br />
=== April 5, Vlad Matei ===<br />
<br />
=== April 12, Micky Steinberg ===<br />
<br />
Title: Groups as metric spaces<br />
<br />
Abstract: Given a group as a set of generators and relations, we can define the “word metric” on the group as the length of the shortest word “between” two elements. This isn’t well-defined, since different generating sets give different metrics, but it is well-defined up to “quasi-isometry”. Come find out what we can do with this! There will lots of pictures and hand-waving!<br />
<br />
=== April 19, Solly Parenti ===<br />
<br />
Title: Elementary Integration<br />
<br />
Abstract: Are you like me? Have you also told your calculus students that finding the antiderivative of e^(-x^2) is impossible? Do you also only have a slight idea about how to prove it? Come find out more about the proof and free yourself of that guilt.<br />
<br />
=== April 26, Ben Bruce ===<br />
<br />
=== May 3, Iván Ongay-Valverde ===<br />
Title: Living with Countable many reals?<br />
<br />
Abstract: Can I make you believe that a countable set of reals are all the reals? If we just have countably many reals, what happens with the others? Do they have any special properties? Let's play a little with our notion of 'reality' and allow to ourselves to find crazy reals doing weird things. Hopefully, no-one's headache will last forever.</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=AMS_Student_Chapter_Seminar&diff=13670AMS Student Chapter Seminar2017-04-17T05:56:08Z<p>Ongay: /* May 3, Iván Ongay-Valverde */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:00 PM – 3:30 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~hast/ Daniel Hast], [https://www.math.wisc.edu/~mrjulian/ Ryan Julian], Cullen McDonald, [https://www.math.wisc.edu/~zcharles/ Zachary Charles]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Spring 2017 ==<br />
<br />
=== January 25, Brandon Alberts ===<br />
<br />
Title: Ultraproducts - they aren't just for logicians<br />
<br />
Abstract: If any of you have attended a logic talk (or one of Ivan's donut seminar talks) you may have learned about ultraproducts as a weird way to mash sets together to get bigger sets in a nice way. Something particularly useful to set theorists, but maybe not so obviously useful to the rest of us. I will give an accessible introduction to ultraproducts and motivate their use in other areas of mathematics.<br />
<br />
=== February 1, Megan Maguire ===<br />
<br />
Title: Hyperbolic crochet workshop<br />
<br />
Abstract: TBA<br />
<br />
=== February 8, Cullen McDonald ===<br />
<br />
=== February 15, Paul Tveite ===<br />
<br />
Title: Fun with Hamel Bases!<br />
<br />
Abstract: If we view the real numbers as a vector field over the rationals, then of course they have a basis (assuming the AOC). This is called a Hamel basis and allows us to do some cool things. Among other things, we will define two periodic functions that sum to the identity function.<br />
<br />
=== February 22, Wil Cocke ===<br />
<br />
Title: Practical Graph Isomorphism<br />
<br />
Abstract: Some graphs are different and some graphs are the same. Sometimes graphs differ only in name. When you give me a graph, you've picked an order. But, is it the same graph across every border?<br />
<br />
=== March 1, Megan Maguire ===<br />
<br />
Title: I stole this talk from Jordan.<br />
<br />
Abstract: Stability is cool! And sometimes things we think don't have stability secretly do. This is an abridged version of a very cool talk I've seen Jordan give a couple times. All credit goes to him. Man, I should have stolen his abstract too.<br />
<br />
=== March 7, Liban Mohamed ===<br />
<br />
Title: Strichartz Estimates from Qualitative to Quantitative<br />
<br />
Abstract: Strichartz estimates are inequalities that give one way understand the decay of solutions to dispersive PDEs. This talk is an attempt to reconcile the formal statements with physical intuition.<br />
<br />
=== March 15, Zachary Charles ===<br />
<br />
Title: Netflix Problem and Chill<br />
<br />
Abstract: How are machine learning, matrix analysis, and Napoleon Dynamite related? Come find out!<br />
<br />
=== April 5, Vlad Matei ===<br />
<br />
=== April 12, Micky Steinberg ===<br />
<br />
Title: Groups as metric spaces<br />
<br />
Abstract: Given a group as a set of generators and relations, we can define the “word metric” on the group as the length of the shortest word “between” two elements. This isn’t well-defined, since different generating sets give different metrics, but it is well-defined up to “quasi-isometry”. Come find out what we can do with this! There will lots of pictures and hand-waving!<br />
<br />
=== April 19, Solly Parenti ===<br />
<br />
Title: Elementary Integration<br />
<br />
Abstract: Are you like me? Have you also told your calculus students that finding the antiderivative of e^(-x^2) is impossible? Do you also only have a slight idea about how to prove it? Come find out more about the proof and free yourself of that guilt.<br />
<br />
=== April 26, Ben Bruce ===<br />
<br />
=== May 3, Iván Ongay-Valverde ===<br />
Different Reals</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Math_222_Spring_2014_Lectures_1_and_2&diff=6912Math 222 Spring 2014 Lectures 1 and 22014-04-21T06:35:15Z<p>Ongay: /* Homework solutions */</p>
<hr />
<div>== Math 222 Spring 2014 ==<br />
<br />
The course web page is located at [http://www.math.wisc.edu/~mmwood/222.html http://www.math.wisc.edu/~mmwood/222.html]. <br />
<br />
===Office hours===<br />
<br />
A list of TAs and their office hours is available at [http://www.math.wisc.edu/~mickysoule/Ta.html http://www.math.wisc.edu/~mickysoule/Ta.html]. Please note that you may attend the office hours of any TA.<br />
<br />
<!--===Midterm review sessions===<br />
<br />
There will be several review sessions held for students leading up to Midterm 1. You can find the times and locations at [http://www.math.wisc.edu/~mickysoule/review1.html http://www.math.wisc.edu/~mickysoule/review1.html]. <br />
--><br />
===Midterm solutions===<br />
<br />
[https://www.dropbox.com/s/deub3loyvmjjuhm/Midterm1Solns.pdf Midterm 1] (27 February 2014)<br />
<br />
[https://www.dropbox.com/s/c53wxg671apggge/midterm2sol.pdf Midterm 2] (8 April 2014)<br />
<br />
===Homework solutions===<br />
<br />
Homework solutions will be posted as they become available:<br />
<br />
[https://mywebspace.wisc.edu/tamorrell/web/Math%20222%20Spring%202014.xapp/files/HW1Solns.pdf Homework 1] (due 23 January 2014)<br />
<br />
[https://www.dropbox.com/s/ate1e5lcg8rzvm7/Calculus%20Notes.pdf Homework 2] (due 30 January 2014)<br />
<br />
[https://mywebspace.wisc.edu/tamorrell/web/Math%20222%20Spring%202014.xapp/files/HW3Solns.pdf Homework 3] (due 6 February 2014)<br />
<br />
[https://www.dropbox.com/s/qx1ehq12adnwj9e/math222week4sol.pdf Homework 4] (due 13 February 2014)<br />
<br />
[https://www.dropbox.com/s/rnfmkzgriw8q63v/Homework6%20solutions.pdf Homework 5] (due 20 February 2014)<br />
<br />
[https://www.dropbox.com/s/582yw35doz8nily/homework%206.pdf Homework 6] (due 6 March 2014)<br />
<br />
[https://www.math.wisc.edu/wiki/images/Math_222_HW_7_solutions.pdf Homework 7] (due 6 March 2014)<br />
<br />
[https://www.dropbox.com/s/elod87f346e3web/HW8.pdf Homework 8] (due 13 March 2014)<br />
<br />
[https://mywebspace.wisc.edu/tamorrell/web/Math%20222%20Spring%202014.xapp/files/Homework09.pdf Homework 9] (due 27 March 2014)<br />
<br />
[https://dl.dropboxusercontent.com/u/58619762/More%20partial%20solutions%20homework%2010.pdf Partial Homework 10] (due Apr 3 2014)</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Math_222_Spring_2014_Lectures_1_and_2&diff=6859Math 222 Spring 2014 Lectures 1 and 22014-04-07T18:43:07Z<p>Ongay: /* Homework solutions */</p>
<hr />
<div>== Math 222 Spring 2014 ==<br />
<br />
The course web page is located at [http://www.math.wisc.edu/~mmwood/222.html http://www.math.wisc.edu/~mmwood/222.html]. <br />
<br />
===Office hours===<br />
<br />
A list of TAs and their office hours is available at [http://www.math.wisc.edu/~mickysoule/Ta.html http://www.math.wisc.edu/~mickysoule/Ta.html]. Please note that you may attend the office hours of any TA.<br />
<br />
<!--===Midterm review sessions===<br />
<br />
There will be several review sessions held for students leading up to Midterm 1. You can find the times and locations at [http://www.math.wisc.edu/~mickysoule/review1.html http://www.math.wisc.edu/~mickysoule/review1.html]. <br />
--><br />
===Midterm solutions===<br />
<br />
[https://www.dropbox.com/s/deub3loyvmjjuhm/Midterm1Solns.pdf Midterm 1] (27 February 2014)<br />
<br />
===Homework solutions===<br />
<br />
Homework solutions will be posted as they become available:<br />
<br />
[https://mywebspace.wisc.edu/tamorrell/web/Math%20222%20Spring%202014.xapp/files/HW1Solns.pdf Homework 1] (due 23 January 2014)<br />
<br />
[https://www.dropbox.com/s/ate1e5lcg8rzvm7/Calculus%20Notes.pdf Homework 2] (due 30 January 2014)<br />
<br />
[https://mywebspace.wisc.edu/tamorrell/web/Math%20222%20Spring%202014.xapp/files/HW3Solns.pdf Homework 3] (due 6 February 2014)<br />
<br />
[https://www.dropbox.com/s/qx1ehq12adnwj9e/math222week4sol.pdf Homework 4] (due 13 February 2014)<br />
<br />
[https://www.dropbox.com/s/rnfmkzgriw8q63v/Homework6%20solutions.pdf Homework 5] (due 20 February 2014)<br />
<br />
[https://www.dropbox.com/s/582yw35doz8nily/homework%206.pdf Homework 6] (due 6 March 2014)<br />
<br />
[https://www.math.wisc.edu/wiki/images/Math_222_HW_7_solutions.pdf Homework 7] (due 6 March 2014)<br />
<br />
[https://www.dropbox.com/s/elod87f346e3web/HW8.pdf Homework 8] (due 13 March 2014)<br />
<br />
[https://mywebspace.wisc.edu/tamorrell/web/Math%20222%20Spring%202014.xapp/files/Homework09.pdf Homework 9] (due 27 March 2014)<br />
<br />
[https://dl.dropboxusercontent.com/u/58619762/Partial%20Solutions%20homework%2010.pdf Partial Homework 10] (due Apr 3 2014)</div>Ongayhttps://www.math.wisc.edu/wiki/index.php?title=Math_222_Spring_2014_Lectures_1_and_2&diff=6858Math 222 Spring 2014 Lectures 1 and 22014-04-07T18:42:23Z<p>Ongay: /* Homework solutions */</p>
<hr />
<div>== Math 222 Spring 2014 ==<br />
<br />
The course web page is located at [http://www.math.wisc.edu/~mmwood/222.html http://www.math.wisc.edu/~mmwood/222.html]. <br />
<br />
===Office hours===<br />
<br />
A list of TAs and their office hours is available at [http://www.math.wisc.edu/~mickysoule/Ta.html http://www.math.wisc.edu/~mickysoule/Ta.html]. Please note that you may attend the office hours of any TA.<br />
<br />
<!--===Midterm review sessions===<br />
<br />
There will be several review sessions held for students leading up to Midterm 1. You can find the times and locations at [http://www.math.wisc.edu/~mickysoule/review1.html http://www.math.wisc.edu/~mickysoule/review1.html]. <br />
--><br />
===Midterm solutions===<br />
<br />
[https://www.dropbox.com/s/deub3loyvmjjuhm/Midterm1Solns.pdf Midterm 1] (27 February 2014)<br />
<br />
===Homework solutions===<br />
<br />
Homework solutions will be posted as they become available:<br />
<br />
[https://mywebspace.wisc.edu/tamorrell/web/Math%20222%20Spring%202014.xapp/files/HW1Solns.pdf Homework 1] (due 23 January 2014)<br />
<br />
[https://www.dropbox.com/s/ate1e5lcg8rzvm7/Calculus%20Notes.pdf Homework 2] (due 30 January 2014)<br />
<br />
[https://mywebspace.wisc.edu/tamorrell/web/Math%20222%20Spring%202014.xapp/files/HW3Solns.pdf Homework 3] (due 6 February 2014)<br />
<br />
[https://www.dropbox.com/s/qx1ehq12adnwj9e/math222week4sol.pdf Homework 4] (due 13 February 2014)<br />
<br />
[https://www.dropbox.com/s/rnfmkzgriw8q63v/Homework6%20solutions.pdf Homework 5] (due 20 February 2014)<br />
<br />
[https://www.dropbox.com/s/582yw35doz8nily/homework%206.pdf Homework 6] (due 6 March 2014)<br />
<br />
[https://www.math.wisc.edu/wiki/images/Math_222_HW_7_solutions.pdf Homework 7] (due 6 March 2014)<br />
<br />
[https://www.dropbox.com/s/elod87f346e3web/HW8.pdf Homework 8] (due 13 March 2014)<br />
<br />
[https://mywebspace.wisc.edu/tamorrell/web/Math%20222%20Spring%202014.xapp/files/Homework09.pdf Homework 9] (due 27 March 2014)<br />
<br />
[https://dl.dropboxusercontent.com/u/58619762/Partial%20Solutions%20homework%2010.pdf] (due Apr 3 2014)</div>Ongay