scholarly journals Langlands duality and global Springer theory

2012 ◽  
Vol 148 (3) ◽  
pp. 835-867 ◽  
Author(s):  
Zhiwei Yun
Keyword(s):  
Chern Class ◽  
Class Action ◽  
Dual Group ◽  
The Other ◽  
Support Theorem ◽  
Langlands Duality ◽  
Dual Groups ◽  
Geometric Langlands ◽  
Springer Theory ◽  
Singular Fibers

AbstractWe compare the cohomology of (parabolic) Hitchin fibers for Langlands dual groups G and G∨. The comparison theorem fits in the framework of the global Springer theory developed by the author. We prove that the stable parts of the parabolic Hitchin complexes for Langlands dual group are naturally isomorphic after passing to the associated graded of the perverse filtration. Moreover, this isomorphism intertwines the global Springer action on one hand and Chern class action on the other. Our result is inspired by the mirror symmetric viewpoint of geometric Langlands duality. Compared to the pioneer work in this subject by T. Hausel and M. Thaddeus, R. Donagi and T. Pantev, and N. Hitchin, our result is valid for more general singular fibers. The proof relies on a variant of Ngô’s support theorem, which is a key point in the proof of the Fundamental Lemma.

scholarly journals Geometric Langlands duality and the equations of Nahm and Bogomolny

2010 ◽  
Vol 140 (4) ◽  
pp. 857-895 ◽  
Author(s):  
Edward Witten
Keyword(s):  
Gauge Theory ◽  
Lie Group ◽  
Moduli Space ◽  
Dual Group ◽  
Langlands Duality ◽  
Geometric Langlands

Geometric Langlands duality relates a representation of a simple Lie group Gv to the cohomology of a certain moduli space associated with the dual group G. In this correspondence, a principal SL2 subgroup of Gv makes an unexpected appearance. This can be explained using gauge theory, as this paper will show, with the help of the equations of Nahm and Bogomolny.

Evaluation of the Therapeutic Effect of Magneto-Nanomicelles Based on Magneto-Thermal and Photo-Thermal Therapy

2020 ◽  
Vol 20 (12) ◽  
pp. 7406-7411
Author(s):  
Weiwen Lin ◽  
Zhizhong Chen ◽  
Jiaoning Fang ◽  
Jingming Chen ◽  
Jiangao Xie ◽  
...  
Keyword(s):  
Tumor Volume ◽  
Aqueous Suspension ◽  
Healing Time ◽  
Dual Group ◽  
Thermal Therapy ◽  
Control Group ◽  
Dual Mode ◽  
Heating Efficiency ◽  
Dual Groups

In this study, we investigated the hyperthermia efficiency of magnetic hyperthermia therapy (MHT), photo-thermal therapy (PTT), and the combination of both techniques by employing SPIO-based magneto-nanomicelles as the heating agents. Magneto-nanomicelles in aqueous suspension were exposed to 808-nm laser irradiation (PTT mode), alternating magnetic field (MHT mode), and both modalities (DUAL mode). All the three methods can offer effective temperature increases (above 20 °C). DUAL-mode resulted in an approximately 2-fold increase in heating efficiency (36 °C) compared with PTT or MHT alone. For in vivo experiments, a total of 24 Lewis carcinoma-bearing mice were randomly divided into four groups: the control group (no therapy), PTT, MHT, and DUAL group. In the three therapy groups, magneto-nanomicelles were injected into the tumor and the corresponding treatment measures were performed every other day for a total of three times each. MRI scans were used to calculate tumor volume after each treatment. One-way analysis of variance (ANOVA) was employed to compare the curative effect of different treatment groups. Compared with the control group, PTT, MHT, and DUAL groups all showed a significant inhibitory effect on tumor volume (P < 0.05). In the DUAL group, the mean tumor volume was smaller than that of the PTT or the MHT group. Our work demonstrated that hyperthermia using SPIO-based magnetonanomicelles has a remarkable suppressive effect in anticancer therapy. Moreover, the combined model of hyperthermia in vivo can achieve synthetic effects with shorter healing time by using the same magneto-nanomicelles.

scholarly journals Springer theory via the Hitchin fibration

2011 ◽  
Vol 147 (5) ◽  
pp. 1635-1670 ◽  
Author(s):  
David Nadler
Keyword(s):  
Fukaya Category ◽  
Group Representations ◽  
Langlands Program ◽  
Geometric Langlands Program ◽  
Constructible Sheaves ◽  
Geometric Langlands ◽  
Springer Theory ◽  
Hitchin Fibration ◽  
Semisimple Complex ◽  
The Fourier Transform

AbstractWe develop the Springer theory of Weyl group representations in the language of symplectic topology. Given a semisimple complex group G, we describe a Lagrangian brane in the cotangent bundle of the adjoint quotient 𝔤/G that produces the perverse sheaves of Springer theory. The main technical tool is an analysis of the Fourier transform for constructible sheaves from the perspective of the Fukaya category. Our results can be viewed as a toy model of the quantization of Hitchin fibers in the geometric Langlands program.

scholarly journals Improving Islamic Students’ Ability on Mastering Names and Responsibilities of Angels through Word Guessing Game

AL-TA LIM ◽  
2017 ◽  
Vol 24 (2) ◽  
pp. 157-164
Author(s):  
Yosmiza Yusra
Keyword(s):  
Action Research ◽  
Learning Outcomes ◽  
Learning Process ◽  
Classical Method ◽  
Disruptive Behaviors ◽  
Learning Model ◽  
Class Action ◽  
The Other ◽  
Research Findings ◽  
Good Learning

From the researcher's experience in the field, many students were reluctant to ask for any clarification, unwilling to express their opinion, less able to give feedback, and did disruptive behaviors during the learning process. Ideally, students are expected to be active and involved in the learning process and to get good learning outcomes. This study is a Class Action Research (CAR), which attempts to improve students' activity and learning outcomes. The research was conducted through four main stages: planning, implementation, monitoring, evaluation and reflection. The research findings from teaching the names and responsibilities of angels through the classical method do not obtain maximum result. On the other hand, word guessing learning model shows better results than that of the classical one. In this model, students are motivated to compete with one another in making and answering the questions. The normally passive students are encouraged to participate actively in learning. Thus, it can be concluded that the learning process with of the game will improve students' learning outcomes

scholarly journals Non metrizable topologies on Z with countable dual group.

2017 ◽  
Vol 18 (1) ◽  
pp. 31
Author(s):  
Daniel De la Barrera Mayoral
Keyword(s):  
Unit Circle ◽  
Complex Plane ◽  
Dual Group ◽  
Independent Interest ◽  
Torsion Subgroup ◽  
Natural Numbers ◽  
Dual Groups

In this paper we give two families of non-metrizable topologies on the group of the integers having a countable dual group which is isomorphic to a infinite torsion subgroup of the unit circle in the complex plane. Both families are related to D-sequences, which are sequences of natural numbers such that each term divides the following. The first family consists of locally quasi-convex group topologies. The second consists of complete topologies which are not locally quasi-convex. In order to study the dual groups for both families we need to make numerical considerations of independent interest.<br /><br />

The Dilemmas of Civil Litigation

1983 ◽  
Vol 18 (2) ◽  
pp. 161-177 ◽  
Author(s):  
J. A. Jolowicz
Keyword(s):  
United States ◽  
American Literature ◽  
Western Europe ◽  
The United States ◽  
Class Action ◽  
The Other ◽  
Class Actions ◽  
American Law ◽  
Time Lead ◽  
Made In

If an English lawyer looks at modern American literature on civil procedure, his first reaction tends to be one of incredulity or incomprehension; the literature deals with subjects of which he has never heard and seeks solutions to questions he has never thought of asking. After some reflection, however, it probably dawns on him that American scholars are writing against a background of assumptions about the process of litigation which he does not share and that those assumptions stem from developments which have occurred in the United States but which have not yet occurred in England or, for that matter, in the other countries of Western Europe. No one in England could write an article such as I received recently from the United States on “Conflict and Dissent in Class Actions” for the simple reason that the class action as it exists in the United States has not yet developed on our side of the Atlantic. Nevertheless, it is now clear that new demands are being made in Europe on the process of litigation, demands which may in time lead to developments such as have already occurred in the United States, and it is these demands which lead to the dilemmas to which my title refers. I want, therefore, to draw attention to two such demands—both very broadly stated—and to the dilemmas they produce, limiting myself mainly to England but with occasional glances elsewhere. This is not a lecture on American law, but it could perhaps be described as one on “pre-American” law.

scholarly journals UPAYA PENINGKATAN KOMPETENSI GURU DALAM MENYUSUN SILABUS DAN RENCANA PELAKSANAAN PEMBELAJARAN (RPP) MELALUI SUPERVISI AKADEMIK YANG BERKELANJUTAN DI SMK NEGERI 4 PADANGSIDIMPUAN

PeTeKa ◽  
2018 ◽  
Vol 1 (3) ◽  
pp. 185
Author(s):  
Budiman Sihombing
Keyword(s):  
Research Methods ◽  
School Principal ◽  
Class Action ◽  
The Other ◽  
Individual Supervision ◽  
Implementation Time ◽  
Planning Implementation ◽  
The City

This research was to look at the percentage of academic supervision the school principal can raise the competence of teachers in the preparation of the syllabus and the RPP. The location of the research is on the CMS State 4 Padangsidimpuan in Jln. Desa Plantations Pijorkoling plantations of Kec. Padangsidimpuan Southeast Of The City Padangsidimpuan. Implementation time is planned for one month starting August 1 to October 30, 2015. This research was carried out on its own writers, and writers assisted by curriculum Developers Team SMK Negeri 4 Padangsidimpuan consisting of the principal, Curriculum, and Waka Waka Studentship. This research was conducted with the research methods class action that lasted for 2 cycles. Each cycle consists of the stages of planning, implementation, observation and reflection. The results obtained, namely the increasing number of good teachers syllabus of 31% to 83% after academic supervision. In addition the number of RPP a good quality also increased from 31% to 89%. Increased competency of teacher in drawing up the syllabus and the RPP is good increased by 52% and 58%. The implementation of individual supervision is suitable to improve the competence of teachers in drawing up the syllabus and RPP during this Administration still remains a difficult requested from our teachers. To test it, we can use the class supervision. For the other trustees are expected to give a clearer input and directional in formation against the teacher.

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